%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/
%% Created for Simon Perdrix at 2017-07-10 11:30:45 -0300
%% Saved with string encoding Unicode (UTF-8)
@inproceedings{gen-supp,
Author = {Jeandel, Emmanuel and Perdrix, Simon and Vilmart, Renaud and Wang, Quanlong},
Booktitle = {42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
Date-Added = {2017-07-10 14:30:31 +0000},
Date-Modified = {2017-07-10 14:30:31 +0000},
Hal_Id = {hal-01445707},
Keywords = {Supplementarity ; Empty Diagram ; Completeness ; ZX-Calculus ; Quantum Information},
Title = {ZX-Calculus: Cyclotomic Supplementarity and Incompleteness for Clifford+T quantum mechanics},
Url = {https://hal.archives-ouvertes.fr/hal-01445707},
Year = {2017},
Bdsk-Url-1 = {https://hal.archives-ouvertes.fr/hal-01445707}}
@article{Hyperfine,
Author = {Ballance, C. J. and Harty, T. P. and Linke, N. M. and Sepiol, M. A. and Lucas, D. M.},
Doi = {10.1103/PhysRevLett.117.060504},
Issue = {6},
Journal = {Phys. Rev. Lett.},
Month = {Aug},
Numpages = {6},
Pages = {060504},
Publisher = {American Physical Society},
Title = {High-Fidelity Quantum Logic Gates Using Trapped-Ion Hyperfine Qubits},
Url = {https://link.aps.org/doi/10.1103/PhysRevLett.117.060504},
Volume = {117},
Year = {2016},
Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.117.060504},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.117.060504}}
@inproceedings{GHZW,
Author = {B. Coecke and A. Kissinger},
Booktitle = {Automata, Languages and Programming},
Note = {{a}r{X}iv:1002.2540},
Pages = {297--308},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {{The compositional structure of multipartite quantum entanglement}},
Year = {2010}}
@article{CPstar,
Author = {Coecke, Bob and Heunen, Chris and Kissinger, Aleks},
Doi = {10.1007/s11128-014-0837-4},
Journal = {Quantum Information Processing},
Number = 12,
Title = {Categories of quantum and classical channels},
Volume = 15,
Year = 2016,
Bdsk-Url-1 = {http://dx.doi.org/10.1007/s11128-014-0837-4}}
@article{NewHope,
Author = {Nick Stratt},
Journal = {The Verge},
Month = {July},
Title = {Google is working to safeguard Chrome from quantum computers},
Year = {2016}}
@Inproceedings{Garvie2017Verifying-the-S,
author = {Garvie, Liam and Duncan, Ross},
year = {2018},
title = {Verifying the Smallest Interesting Colour Code with Quantomatic},
editor = {Coecke, Bob and Kissinger, Aleks},
booktitle = {{\rm Proceedings 14th International Conference on}
Quantum Physics and Logic,
{\rm Nijmegen, The Netherlands, 3-7 July 2017}},
series = {Electronic Proceedings in Theoretical Computer Science},
volume = {266},
publisher = {Open Publishing Association},
pages = {147-163},
doi = {10.4204/EPTCS.266.10},
}
@unpublished{BH-2017,
Author = {Niel de Beaudrap and Dominic Horsman},
Note = {arXiv:1704.08670},
Title = {The {ZX} calculus is a language for surface code lattice surgery},
Year = {2017}}
@unpublished{NgWang,
Author = {Kang Feng Ng and Quanlong Wang},
Note = {arXiv:1706.09877},
Title = {A universal completion of the ZX-calculus},
Year = {2017}}
@InProceedings{HFW,
author = {Amar Hadzihasanovic and Kang Feng Ng and Quanlong Wang},
title = {Two complete axiomatisations of pure-state qubit quantum computing},
booktitle = "ACM/IEEE Symposium on
Logic in Computer Science (LICS)",
year = 2018}
@InProceedings{JPV-2018,
author = {Emmanuel Jeandel and Simon Perdrix and Renaud Vilmart},
title = {Diagrammatic Reasoning beyond {Clifford+T} Quantum Mechanics},
booktitle = "ACM/IEEE Symposium on
Logic in Computer Science (LICS)",
year = 2018}
@InProceedings{Jeandel2017A-Complete-Axio,
author = {Emmanuel Jeandel and Simon Perdrix and Renaud Vilmart},
title = {A Complete Axiomatisation of the {ZX}-Calculus for {C}lifford+{T} Quantum Mechanics},
booktitle = "ACM/IEEE Symposium on
Logic in Computer Science (LICS)",
year = 2018}
@article{KendonAncilla,
Author = {Proctor, Timothy J. and Andersson, Erika and Kendon, Viv},
Doi = {10.1103/PhysRevA.88.042330},
Issue = {4},
Journal = {Phys. Rev. A},
Month = {Oct},
Numpages = {9},
Pages = {042330},
Publisher = {American Physical Society},
Title = {Universal quantum computation by the unitary control of ancilla qubits and using a fixed ancilla-register interaction},
Url = {http://link.aps.org/doi/10.1103/PhysRevA.88.042330},
Volume = {88},
Year = {2013},
Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevA.88.042330},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevA.88.042330}}
@inproceedings{Hadzihasanovic2017A-Topological-P,
Author = {Amar Hadzihasanovic},
Booktitle = {Proceedings QPL 2016},
Citation_Arxiv_Id = {1701.00658},
Citation_Author = {Hadzihasanovic, Amar},
Citation_Date = {2017/01/03},
Citation_Doi = {10.4204/EPTCS.236.5},
Citation_Online_Date = {2017/01/03},
Citation_Pdf_Url = {http://arxiv.org/pdf/1701.00658},
Citation_Title = {A Topological Perspective on Interacting Algebraic Theories},
Date-Added = {2017-03-07 13:16:07 +0000},
Date-Modified = {2017-03-07 13:16:07 +0000},
Doi = {10.4204/EPTCS.236.5},
Pages = {70-86},
Series = {EPTCS},
Title = {A Topological Perspective on Interacting Algebraic Theories},
Volume = {236},
Year = {2017},
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Bdsk-Url-1 = {http://dx.doi.org/10.4204/EPTCS.236.5}}
@InProceedings{jeandelicalp2004,
author = "Emmanuel Jeandel",
title = "{Universality in Quantum Computation}",
volume = "3142",
series = "Lecture Notes in Computer Science",
booktitle = "International Colloquium on Automata, Languages and Programming (ICALP)",
year = "2004",
publisher = "Springer",
pages = "793--804",
doi = "10.1007/978-3-540-27836-8_67",
keywords = "Quantum circuits, Universality, Algebraic Geometry",
}
@article{Stefano-Gogioso2017Fully-graphical,
Abstract = {The abelian Hidden Subgroup Problem (HSP) is extremely general, and many problems with known quantum exponential speed-up (such as integers factorisation, the discrete logarithm and Simon's problem) can be seen as specific instances of it. The traditional presentation of the quantum protocol for the abelian HSP is low-level, and relies heavily on the the interplay between classical group theory and complex vector spaces. Instead, we give a high-level diagrammatic presentation which showcases the quantum structures truly at play. Specifically, we provide the first fully diagrammatic proof of correctness for the abelian HSP protocol, showing that strongly complementary observables are the key ingredient to its success. Being fully diagrammatic, our proof extends beyond the traditional case of finite-dimensional quantum theory: for example, we can use it to show that Simon's problem can be efficiently solved in real quantum theory, and to obtain a protocol that solves the HSP for certain infinite abelian groups.},
Author = {Stefano Gogioso and Aleks Kissinger},
Citation_Arxiv_Id = {1701.08669},
Citation_Author = {Kissinger, Aleks},
Citation_Date = {2017/01/30},
Citation_Online_Date = {2017/01/30},
Citation_Pdf_Url = {http://arxiv.org/pdf/1701.08669},
Citation_Title = {Fully graphical treatment of the quantum algorithm for the Hidden Subgroup Problem},
Date-Added = {2017-03-07 13:13:40 +0000},
Date-Modified = {2017-03-07 13:13:40 +0000},
Eprint = {arXiv:1701.08669},
Journal = {arXiv.org},
Number = {1701.08669},
Title = {Fully graphical treatment of the quantum algorithm for the Hidden Subgroup Problem},
Year = {2017},
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@misc{Cross2017Open-Quantum-As,
Author = {Andrew W. Cross and Lev S. Bishop and John A. Smolin and Jay M. Gambetta},
Date-Added = {2017-03-05 21:01:08 +0000},
Date-Modified = {2017-03-05 21:03:10 +0000},
Howpublished = {\url{https://arXiv.org/abs/arXiv:1707.03429}},
Keywords = {QASM, quantum computing, programming language},
Month = {January},
Title = {Open Quantum Assembly Language},
Year = {2017},
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@misc{llvm:website,
Date-Added = {2017-03-05 13:17:20 +0000},
Date-Modified = {2017-03-05 13:28:46 +0000},
Title = {The {LLVM} Compiler Infrastructure},
Url = {http://llvm.org},
Bdsk-Url-1 = {http://llvm.org}}
@misc{IBMQuantumExp,
Date-Added = {2017-03-04 20:28:44 +0000},
Date-Modified = {2017-03-05 13:28:53 +0000},
Howpublished = {http://research.ibm.com/quantum/},
Title = {{IBM} Quantum Experience}}
@article{ALTENKIRCH200723,
Abstract = {We develop a sound and complete equational theory for the functional quantum programming language QML. The soundness and completeness of the theory are with respect to the previously developed denotational semantics of QML. The completeness proof also gives rise to a normalisation algorithm following the normalisation-by-evaluation approach. The current work focuses on the pure fragment of QML, omitting measurements.},
Author = {Thorsten Altenkirch and Jonathan Grattage and Juliana K. Vizzotto and Amr Sabry},
Date-Added = {2017-03-04 14:21:29 +0000},
Date-Modified = {2017-03-04 14:21:57 +0000},
Doi = {10.1016/j.entcs.2006.12.010},
Issn = {1571-0661},
Journal = {Electronic Notes in Theoretical Computer Science},
Keywords = {normalisation},
Pages = {23 - 47},
Title = {An Algebra of Pure Quantum Programming},
Url = {http://www.sciencedirect.com/science/article/pii/S1571066107000540},
Volume = {170},
Year = {2007},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S1571066107000540},
Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.entcs.2006.12.010}}
@inproceedings{Paykin2017a,
Address = {New York, NY, USA},
Author = {Paykin, Jennifer and Rand, Robert and Zdancewic, Steve},
Booktitle = {Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages},
Date-Added = {2017-03-04 13:55:29 +0000},
Date-Modified = {2017-03-06 05:51:27 +0000},
Doi = {10.1145/3009837.3009894},
Location = {Paris, France},
Numpages = {13},
Pages = {846--858},
Publisher = {ACM},
Series = {POPL 2017},
Title = {{QWIRE}: A Core Language for Quantum Circuits},
Year = {2017},
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Bdsk-Url-1 = {http://dx.doi.org/10.1145/3009837.3009894}}
@article{Mlnarik2007Operational-Sem,
Author = {Hynek Mlnarik},
Citation_Arxiv_Id = {0708.0890},
Citation_Author = {Mlnarik, Hynek},
Citation_Date = {2007/08/07},
Citation_Online_Date = {2007/08/07},
Citation_Pdf_Url = {http://arxiv.org/pdf/0708.0890},
Citation_Title = {Operational Semantics and Type Soundness of Quantum Programming Language LanQ},
Date-Added = {2017-03-04 13:53:10 +0000},
Date-Modified = {2017-03-04 13:53:10 +0000},
Eprint = {arXiv:0708.0890},
Journal = {arXiv.org},
Number = {0708.0890},
Title = {Operational Semantics and Type Soundness of Quantum Programming Language LanQ},
Year = {2007},
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@article{PhysRevX.4.041041,
Author = {Nickerson, Naomi H. and Fitzsimons, Joseph F. and Benjamin, Simon C.},
Date-Added = {2017-03-04 13:40:41 +0000},
Date-Modified = {2017-03-04 13:40:41 +0000},
Doi = {10.1103/PhysRevX.4.041041},
Issue = {4},
Journal = {Phys. Rev. X},
Month = {Dec},
Numpages = {17},
Pages = {041041},
Publisher = {American Physical Society},
Title = {Freely Scalable Quantum Technologies Using Cells of 5-to-50 Qubits with Very Lossy and Noisy Photonic Links},
Url = {http://link.aps.org/doi/10.1103/PhysRevX.4.041041},
Volume = {4},
Year = {2014},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevX.4.041041},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevX.4.041041}}
@article{Versluis2016Scalable-quantu,
Abstract = {We present a scalable scheme for executing the error-correction cycle of a monolithic surface-code fabric composed of fast-flux-tuneable transmon qubits with nearest-neighbor coupling. An eight-qubit unit cell forms the basis for repeating both the quantum hardware and coherent control, enabling spatial multiplexing. This control uses three fixed frequencies for all single-qubit gates and a unique frequency detuning pattern for each qubit in the cell. By pipelining the interaction and readout steps of ancilla-based XX- and ZZ-type stabilizer measurements, we can engineer detuning patterns that avoid all second-order transmon-transmon interactions except those exploited in controlled-phase gates, regardless of fabric size. Our scheme is applicable to defect-based and planar logical qubits, including lattice surgery.},
Author = {R. Versluis and S. Poletto and N. Khammassi and N. Haider and D. J. Michalak and A. Bruno and K. Bertels and L. DiCarlo},
Citation_Arxiv_Id = {1612.08208},
Citation_Author = {DiCarlo, L.},
Citation_Date = {2016/12/24},
Citation_Online_Date = {2016/12/24},
Citation_Pdf_Url = {http://arxiv.org/pdf/1612.08208},
Citation_Title = {Scalable quantum circuit and control for a superconducting surface code},
Date-Added = {2017-03-04 13:25:59 +0000},
Date-Modified = {2017-03-04 13:25:59 +0000},
Eprint = {arXiv:1612.08208},
Journal = {arXiv.org},
Number = {1612.08208},
Title = {Scalable quantum circuit and control for a superconducting surface code},
Year = {2016},
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@article{Hner2016A-Software-Meth,
Abstract = {Quantum computers promise to transform our notions of computation by offering a completely new paradigm. To achieve scalable quantum computation, optimizing compilers and a corresponding software design flow will be essential. We present a software architecture for compiling quantum programs from a high-level language program to hardware-specific instructions. We describe the necessary layers of abstraction and their differences and similarities to classical layers of a computer-aided design flow. For each layer of the stack, we discuss the underlying methods for compilation and optimization. Our software methodology facilitates more rapid innovation among quantum algorithm designers, quantum hardware engineers, and experimentalists. It enables scalable compilation of complex quantum algorithms and can be targeted to any specific quantum hardware implementation.},
Author = {Thomas H\"aner and Damian S. Steiger and Krysta Svore and Matthias Troyer},
Citation_Arxiv_Id = {1604.01401},
Citation_Author = {Troyer, Matthias},
Citation_Date = {2016/04/05},
Citation_Online_Date = {2016/05/11},
Citation_Pdf_Url = {http://arxiv.org/pdf/1604.01401},
Citation_Title = {A Software Methodology for Compiling Quantum Programs},
Date-Added = {2017-03-04 12:56:09 +0000},
Date-Modified = {2017-03-06 05:28:51 +0000},
Eprint = {arXiv:1604.01401},
Journal = {arXiv.org},
Number = {1604.01401},
Title = {A Software Methodology for Compiling Quantum Programs},
Year = {2016},
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@article{Steiger2016ProjectQ:-An-Op,
doi = {10.22331/q-2018-01-31-49},
title = {Project{Q}: an open source software framework for quantum computing},
author = {Steiger, Damian S. and H{\"{a}}ner, Thomas and Troyer, Matthias},
journal = {{Quantum}},
issn = {2521-327X},
publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
volume = {2},
pages = {49},
month = jan,
year = {2018}
}
@article{1703.00466,
Author = {J.~Bermejo-Vega and D.~Hangleiter and M.~Schwarz and R.~Raussendorf and J.~Eisert},
Date-Added = {2017-03-03 06:46:11 +0000},
Date-Modified = {2017-03-03 06:47:06 +0000},
Eprint = {arXiv:1703.00466},
Journal = {ArXiv.org},
Number = {1703.00466},
Title = {{A}rchitectures for quantum simulation showing quantum supremacy},
Year = {2017},
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@inproceedings{Yokoyama:2007:RPL:1244381.1244404,
Address = {New York, NY, USA},
Author = {Yokoyama, Tetsuo and Gl\"{u}ck, Robert},
Booktitle = {Proceedings of the 2007 ACM SIGPLAN Symposium on Partial Evaluation and Semantics-based Program Manipulation},
Date-Added = {2017-02-28 11:03:52 +0000},
Date-Modified = {2017-02-28 11:04:14 +0000},
Doi = {10.1145/1244381.1244404},
Isbn = {978-1-59593-620-2},
Keywords = {Janus, non-standard interpreter hierarchy, program inversion, reversible computing, reversible programming language, self-interpreter},
Pages = {144--153},
Publisher = {ACM},
Series = {PEPM '07},
Title = {A Reversible Programming Language and Its Invertible Self-interpreter},
Url = {http://doi.acm.org/10.1145/1244381.1244404},
Year = {2007},
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Bdsk-Url-1 = {http://doi.acm.org/10.1145/1244381.1244404},
Bdsk-Url-2 = {http://dx.doi.org/10.1145/1244381.1244404}}
@article{Parent2015Reversible-circ,
Abstract = {We develop a framework for resource efficient compilation of higher-level programs into lower-level reversible circuits. Our main focus is on optimizing the memory footprint of the resulting reversible networks. This is motivated by the limited availability of qubits for the foreseeable future. We apply three main techniques to keep the number of required qubits small when computing classical, irreversible computations by means of reversible networks: first, wherever possible we allow the compiler to make use of in-place functions to modify some of the variables. Second, an intermediate representation is introduced that allows to trace data dependencies within the program, allowing to clean up qubits early. This realizes an analog to "garbage collection" for reversible circuits. Third, we use the concept of so-called pebble games to transform irreversible programs into reversible programs under space constraints, allowing for data to be erased and recomputed if needed. We introduce REVS, a compiler for reversible circuits that can translate a subset of the functional programming language F# into Toffoli networks which can then be further interpreted for instance in LIQui|>, a domain-specific language for quantum computing and which is also embedded into F#. We discuss a number of test cases that illustrate the advantages of our approach including reversible implementations of SHA-2 and other cryptographic hash-functions, reversible integer arithmetic, as well as a test-bench of combinational circuits used in classical circuit synthesis. Compared to Bennett's method, REVS can reduce space complexity by a factor of 44 or more, while having an only moderate increase in circuit size as well as in the time it takes to compile the reversible networks.},
Author = {Alex Parent and Martin Roetteler and Krysta M. Svore},
Citation_Arxiv_Id = {1510.00377},
Citation_Author = {Svore, Krysta M.},
Citation_Date = {2015/10/01},
Citation_Online_Date = {2015/10/01},
Citation_Pdf_Url = {http://arxiv.org/pdf/1510.00377},
Citation_Title = {Reversible circuit compilation with space constraints},
Date-Added = {2017-02-28 11:01:50 +0000},
Date-Modified = {2017-02-28 11:01:50 +0000},
Eprint = {arXiv:1510.00377},
Journal = {arXiv.org},
Number = {1510.00377},
Title = {Reversible circuit compilation with space constraints},
Year = {2015},
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@inproceedings{Perdrix2008,
Address = {Berlin, Heidelberg},
Author = {Perdrix, Simon},
Booktitle = {Static Analysis: 15th International Symposium, SAS 2008, Valencia, Spain, July 16-18, 2008. Proceedings},
Date-Added = {2017-02-28 10:58:49 +0000},
Date-Modified = {2017-02-28 10:59:01 +0000},
Doi = {10.1007/978-3-540-69166-2_18},
Isbn = {978-3-540-69166-2},
Pages = {270--282},
Publisher = {Springer Berlin Heidelberg},
Title = {Quantum Entanglement Analysis Based on Abstract Interpretation},
Url = {http://dx.doi.org/10.1007/978-3-540-69166-2_18},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-540-69166-2_18}}
@article{Marion2009Sup-interpretat,
Author = {Jean-Yves Marion and Romain P\'echoux},
Date-Added = {2017-02-28 10:57:54 +0000},
Date-Modified = {2017-02-28 10:57:54 +0000},
Doi = {10.1145/1555746.1555751},
Journal = {ACM Trans. Comput. Log.},
Number = {4},
Title = {Sup-interpretations, a semantic method for static analysis of program resources},
Volume = {10},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1145/1555746.1555751}}
@article{Gaboardi:2012:ICP:2159531.2159540,
Author = {Gaboardi, Marco and Marion, Jean-Yves and Ronchi Della Rocca, Simona},
Date-Added = {2017-02-28 10:52:13 +0000},
Date-Modified = {2017-02-28 10:52:44 +0000},
Doi = {10.1145/2159531.2159540},
Issn = {1529-3785},
Journal = {ACM Trans. Comput. Logic},
Keywords = {Implicit computational complexity, linear logic, operational semantics, polynomial space, type assignment},
Number = {2},
Pages = {18:1--18:36},
Publisher = {ACM},
Title = {An Implicit Characterization of PSPACE},
Url = {http://doi.acm.org/10.1145/2159531.2159540},
Volume = {13},
Year = {2012},
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Bdsk-Url-1 = {http://doi.acm.org/10.1145/2159531.2159540},
Bdsk-Url-2 = {http://dx.doi.org/10.1145/2159531.2159540}}
@article{DALLAGO2010377,
Abstract = {We introduce a quantum lambda calculus inspired by Lafont's Soft Linear Logic and capturing the polynomial quantum complexity classes EQP, BQP and ZQP. The calculus is based on the ``classical control and quantum data'' paradigm. This is the first example of a formal system capturing quantum complexity classes in the spirit of implicit computational complexity --- it is machine-free and no explicit bound (e.g., polynomials) appears in its syntax.},
Author = {Ugo Dal Lago and Andrea Masini and Margherita Zorzi},
Date-Added = {2017-02-28 10:47:34 +0000},
Date-Modified = {2017-02-28 10:47:34 +0000},
Doi = {http://dx.doi.org/10.1016/j.tcs.2009.07.045},
Issn = {0304-3975},
Journal = {Theoretical Computer Science},
Keywords = {Lambda calculus},
Number = {2},
Pages = {377 - 409},
Title = {Quantum implicit computational complexity},
Url = {http://www.sciencedirect.com/science/article/pii/S0304397509005167},
Volume = {411},
Year = {2010},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0304397509005167},
Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.tcs.2009.07.045}}
@article{Assaf2014Call-by-value-c,
Abstract = {We examine the relationship between the algebraic lambda-calculus, a fragment of the differential lambda-calculus and the linear-algebraic lambda-calculus, a candidate lambda-calculus for quantum computation. Both calculi are algebraic: each one is equipped with an additive and a scalar-multiplicative structure, and their set of terms is closed under linear combinations. However, the two languages were built using different approaches: the former is a call-by-name language whereas the latter is call-by-value; the former considers algebraic equalities whereas the latter approaches them through rewrite rules. In this paper, we analyse how these different approaches relate to one another. To this end, we propose four canonical languages based on each of the possible choices: call-by-name versus call-by-value, algebraic equality versus algebraic rewriting. We show that the various languages simulate one another. Due to subtle interaction between beta-reduction and algebraic rewriting, to make the languages consistent some additional hypotheses such as confluence or normalisation might be required. We carefully devise the required properties for each proof, making them general enough to be valid for any sub-language satisfying the corresponding properties.},
Author = {Ali Assaf and Alejandro D\'iaz-Caro and Simon Perdrix and Christine Tasson and Beno\^it Valiron},
Date-Added = {2017-02-28 10:25:20 +0000},
Date-Modified = {2017-02-28 10:46:31 +0000},
Doi = {10.2168/LMCS-10(4:8)2014},
Eprint = {arXiv:1005.2897},
Number = {4},
Title = {Call-by-value, call-by-name and the vectorial behaviour of the algebraic $\lambda$-calculus},
Volume = {10},
Year = {2014},
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Bdsk-Url-1 = {http://dx.doi.org/10.2168/LMCS-10(4:8)2014}}
@inproceedings{Hadzihasanovic2015A-Diagrammatic-,
Abstract = {Diagrammatic techniques for reasoning about monoidal categories provide an intuitive understanding of the symmetries and connections of interacting computational processes. In the context of categorical quantum mechanics, Coecke and Kissinger suggested that two 3-qubit states, GHZ and W, may be used as the building blocks of a new graphical calculus, aimed at a diagrammatic classification of multipartite qubit entanglement that would highlight the communicational properties of quantum states, and their potential uses in cryptographic schemes. In this paper, we present a full graphical axiomatisation of the relations between GHZ and W: the ZW calculus. This refines a version of the preexisting ZX calculus, while keeping its most desirable characteristics: undirected ness, a large degree of symmetry, and an algebraic underpinning. We prove that the ZW calculus is complete for the category of free abelian groups on a power of two generators -- "qubits with integer coefficients" -- and provide an explicit normalisation procedure.},
Author = {Amar Hadzihasanovic},
Booktitle = {2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
Citation_Author = {Amar Hadzihasanovic},
Citation_Conference = {2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
Citation_Doi = {10.1109/LICS.2015.59},
Citation_Firstpage = {573},
Citation_Isbn = {978-1-4799-8875-4},
Citation_Issn = {1043-6871},
Citation_Keywords = {SLOCC classification; categorical quantum mechanics; string diagrams; compact closed categories; multipartite entanglement;},
Citation_Language = {English},
Citation_Lastpage = {584},
Citation_Pdf_Url = {http://www.computer.org/csdl/proceedings/lics/2015/8875/00/8875a573.pdf},
Citation_Publication_Date = {2015-07-01},
Citation_Publisher = {IEEE},
Citation_Title = {A Diagrammatic Axiomatisation for Qubit Entanglement},
Date-Added = {2017-01-31 12:30:49 +0000},
Date-Modified = {2017-01-31 12:32:39 +0000},
Dc.Creator = {Amar Hadzihasanovic},
Dc.Date = {2015-07-01},
Dc.Description = {Diagrammatic techniques for reasoning about monoidal categories provide an intuitive understanding of the symmetries and connections of interacting computational processes. In the context of categorical quantum mechanics, Coecke and Kissinger suggested that two 3-qubit states, GHZ and W, may be used as the building blocks of a new graphical calculus, aimed at a diagrammatic classification of multipartite qubit entanglement that would highlight the communicational properties of quantum states, and their potential uses in cryptographic schemes. In this paper, we present a full graphical axiomatisation of the relations between GHZ and W: the ZW calculus. This refines a version of the preexisting ZX calculus, while keeping its most desirable characteristics: undirected ness, a large degree of symmetry, and an algebraic underpinning. We prove that the ZW calculus is complete for the category of free abelian groups on a power of two generators -- "qubits with integer coefficients" -- and provide an explicit normalisation procedure.},
Dc.Format = {text/html},
Dc.Identifier = {1043-6871},
Dc.Publisher = {IEEE Computer Society},
Dc.Relation.Ispartof = {2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
Dc.Title = {A Diagrammatic Axiomatisation for Qubit Entanglement},
Dc.Type = {text},
Description = {Diagrammatic techniques for reasoning about monoidal categories provide an intuitive understanding of the symmetries and connections of interacting computational processes. In the context of categorical quantum mechanics, Coecke and Kissinger suggested that two 3-qubit states, GHZ and W, may be used as the building blocks of a new graphical calculus, aimed at a diagrammatic classification of multipartite qubit entanglement that would highlight the communicational properties of quantum states, and their potential uses in cryptographic schemes. In this paper, we present a full graphical axiomatisation of the relations between GHZ and W: the ZW calculus. This refines a version of the preexisting ZX calculus, while keeping its most desirable characteristics: undirected ness, a large degree of symmetry, and an algebraic underpinning. We prove that the ZW calculus is complete for the category of free abelian groups on a power of two generators -- "qubits with integer coefficients" -- and provide an explicit normalisation procedure.},
Doi = {10.1109/LICS.2015.59},
Eprint = {arXiv:1501.07082},
Keywords = {SLOCC classification; categorical quantum mechanics; string diagrams; compact closed categories; multipartite entanglement;},
Pages = {573-584},
Title = {A Diagrammatic Axiomatisation for Qubit Entanglement},
Viewport = {width=device-width, initial-scale=1, maximum-scale=1},
Year = {2015},
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@phdthesis{GraydonThesis2017,
Abstract = {Physical theories can be characterized in terms of their state spaces and their evolutive equations. The kinematical structure and the dynamical structure of finite dimensional quantum theory are, in light of the Choi-Jamiolkowski isomorphism, one and the same --- namely the homogeneous self-dual cones of positive semi-definite linear endomorphisms on finite dimensional complex Hilbert spaces. From the perspective of category theory, these cones are the sets of morphisms in finite dimensional quantum theory as a dagger compact closed category. Understanding the intricate geometry of these cones and charting the wider landscape for their host category is imperative for foundational physics.
In Part I of this thesis, we study the shape of finite dimensional quantum theory in terms of quantum information. We introduce novel geometric structures inscribed within quantum cones: conical t-designs. Conical t-designs are a natural, strictly inclusive generalization of complex projective t-designs. We prove that symmetric informationally complete measurements of arbitrary rank (SIMs), and full sets of mutually unbiased measurements of arbitrary rank (MUMs) are conical 2-designs. SIMs and MUMs correspond to highly symmetric polytopes within the Bloch body. The same holds for the entire class of homogeneous conical 2-designs; moreover, we establish necessary and sufficient conditions for a Bloch polytope to represent a homogeneous conical 2-design. Furthermore, we show that infinite families of such designs exist in all finite dimensions. It turns out that conical 2-designs are naturally adapted to a geometric description of bipartite entanglement. We prove that a quantum measurement is a conical 2-design if and only if there exists a (regular) entanglement monotone whose restriction to pure states is a function of the norm of the probability vector over the outcomes of the bipartite measurement formed from its tensor products. In that case the concurrence is such a monotone. In addition to monotones, we formulate entanglement witnesses in terms of geometric conditions on the aforementioned conical 2-design probabilities.
In Part II of this thesis, we move beyond quantum theory within the vein of Euclidean Jordan algebras (EJAs). In light of the Koecher-Vinberg theorem, the positive cones of EJAs are the only homogeneous self-dual cones to be found in a finite dimensional setting. We consider physical theories based on EJAs subject to nonsignaling axioms regarding their compositional structure. We prove that any such Jordanic composite is a Jordan ideal of Hanche-Olsen's universal tensor product. Consequently, no Jordanic composite exists having the exceptional Jordan algebra as a direct summand, nor does any such composite exist if either factor is exceptional. So we focus on special EJAs of self-adjoint matrices over the real, complex, and quaternionic division rings. We demonstrate that these can be organized in a natural way as a symmetric monoidal category, albeit one that is not compact closed. We then construct a related category InvQM of embedded EJAs, having fewer objects but more morphisms, that is dagger compact closed. This category unifies finite dimensional real, complex and quaternionic quantum theories, except that the composite of two complex quantum systems comes with an extra classical bit. Our notion of composite requires neither tomographic locality, nor preservation of purity under monoidal products. The categories we construct include examples in which both of these conditions fail. Our unification cannot be extended to include any finite dimensional spin factors (save the rebit, qubit, and quabit) without destroying compact closure.
},
Author = {Matthew Graydon},
Date-Added = {2017-01-13 18:00:52 +0000},
Date-Modified = {2017-01-13 18:02:19 +0000},
School = {University of Waterloo},
Title = {Conical Designs and Categorical {J}ordan Algebraic Post-Quantum Theories},
Year = {2017},
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@inproceedings{7174912,
Abstract = {We study multitoken interaction machines in the context of a very expressive linear logical system with exponentials, fix points and synchronization. The advantage of such machines is to provide models in the style of the Geometry of Interaction, i.e., An interactive semantics which is close to low-level implementation. On the one hand, we prove that despite the inherent complexity of the framework, interaction is guaranteed to be deadlock-free. On the other hand, the resulting logical system is powerful enough to embed PCF and to adequately model its behaviour, both when call-by-name and when call-by-value evaluation are considered. This is not the case for single-token stateless interactive machines.},
Author = {U. D. Lago and C. Faggian and B. Valiron and A. Yoshimizu},
Booktitle = {2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science},
Date-Added = {2016-12-27 17:33:48 +0000},
Date-Modified = {2016-12-27 17:33:48 +0000},
Doi = {10.1109/LICS.2015.58},
Issn = {1043-6871},
Keywords = {interactive systems;logic programming;parallel programming;synchronisation;deadlock-free;geometry of interaction;infinitary context;interactive semantics;linear logical system;multitoken interaction machines;parallelism;single-token stateless interactive machines;synchronization;Context;Geometry;Machinery;Parallel processing;Semantics;Synchronization;System recovery;Abstract Machines;Geometry of Interaction;Linear Logic;Parallel Computation},
Month = {July},
Pages = {559-572},
Title = {Parallelism and Synchronization in an Infinitary Context},
Year = {2015},
Bdsk-Url-1 = {http://dx.doi.org/10.1109/LICS.2015.58}}
@inproceedings{Valiron2016,
Author = {Valiron, Beno{\^\i}t},
Booktitle = {Reversible Computation: 8th International Conference, RC 2016, Bologna, Italy, July 7-8, 2016, Proceedings},
Date-Added = {2016-12-27 17:31:22 +0000},
Date-Modified = {2016-12-27 17:32:08 +0000},
Doi = {10.1007/978-3-319-40578-0_21},
Editor = {Devitt, Simon and Lanese, Ivan},
Isbn = {978-3-319-40578-0},
Pages = {289--306},
Publisher = {Springer International Publishing},
Title = {Generating Reversible Circuits from Higher-Order Functional Programs},
Year = {2016},
Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-319-40578-0_21}}
@article{Valiron:2015:PQF:2808213.2699415,
Acmid = {2699415},
Address = {New York, NY, USA},
Author = {Valiron, Beno\^{\i}t and Ross, Neil J. and Selinger, Peter and Alexander, D. Scott and Smith, Jonathan M.},
Date-Added = {2016-12-27 17:30:38 +0000},
Date-Modified = {2016-12-27 17:30:38 +0000},
Doi = {10.1145/2699415},
Issn = {0001-0782},
Issue_Date = {August 2015},
Journal = {Commun. ACM},
Month = jul,
Number = {8},
Numpages = {10},
Pages = {52--61},
Publisher = {ACM},
Title = {Programming the Quantum Future},
Url = {http://doi.acm.org/10.1145/2699415},
Volume = {58},
Year = {2015},
Bdsk-Url-1 = {http://doi.acm.org/10.1145/2699415},
Bdsk-Url-2 = {http://dx.doi.org/10.1145/2699415}}
@article{Chancellor2016Coherent-Parity,
Abstract = {We present a framework for constructing and analysing quantum error correction codes that gives simple and intuitive tools for designing codes based on device specifications. Built from a direct analog of classical parity checking, these coherent parity codes use a simple model for constraints between qubits and decoding of information. With an associated graphical language, this coherent parity check (CPC) construction enables automated search for codes, and we give discovered examples of low-overhead codes for small devices ([[10,3,3]], and [[12,4,3]]) based on realistic error rates taken from current ion trap state-of-the-art . We show that CPC codes form a class of CSS codes. We further show that the graphical language maps to the category-theoretic ZX calculus, which enables the use of the automated reasoning tool Quantomatic to derive properties of the codes. We show how automated reasoning allows us to perform computation between qubits in the same code-block without requiring multiple codeblocks and/or transversal gates. These tools offer a significant aid to put quantum error correction theory into design practice for practical quantum technologies in both the immediate future and looking forwards to large-scale deployable quantum computing. Furthermore, the close theoretical link between the CPC construction and classical error correction codes opens up the possibility of constructing quantum versions of modern high- performance error correction codes (such as LDPC and turbo codes) that approach the Shannon limit.},
Author = {Nicholas Chancellor and Aleks Kissinger and Joschka Roffe and Stefan Zohren and Dominic Horsman},
Citation_Arxiv_Id = {1611.08012},
Citation_Author = {Horsman, Dominic},
Citation_Date = {2016/11/23},
Citation_Online_Date = {2016/11/23},
Citation_Pdf_Url = {http://arxiv.org/pdf/1611.08012},
Citation_Title = {Graphical Structures for Design and Verification of Quantum Error Correction},
Date-Added = {2016-12-24 11:21:45 +0000},
Date-Modified = {2016-12-24 11:21:45 +0000},
Eprint = {arXiv:1611.08012},
Journal = {arXiv.org},
Number = {1611.08012},
Title = {Graphical Structures for Design and Verification of Quantum Error Correction},
Year = {2016},
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@article{MILNER19921,
Abstract = {We present the π-calculus, a calculus of communicating systems in which one can naturally express processes which have changing structure. Not only may the component agents of a system be arbitrarily linked, but a communication between neighbours may carry information which changes that linkage. The calculus is an extension of the process algebra CCS, following work by Engberg and Nielsen, who added mobility to CCS while preserving its algebraic properties. The π-calculus gains simplicity by removing all distinction between variables and constants; communication links are identified by names, and computation is represented purely as the communication of names across links. After an illustrated description of how the π-calculus generalises conventional process algebras in treating mobility, several examples exploiting mobility are given in some detail. The important examples are the encoding into the π-calculus of higher-order functions (the λ-calculus and combinatory algebra), the transmission of processes as values, and the representation of data structures as processes. The paper continues by presenting the algebraic theory of strong bisimilarity and strong equivalence, including a new notion of equivalence indexed by distinctions---i.e., assumptions of inequality among names. These theories are based upon a semantics in terms of a labeled transition system and a notion of strong bisimulation, both of which are expounded in detail in a companion paper. We also report briefly on work-in-progress based upon the corresponding notion of weak bisimulation, in which internal actions cannot be observed.},
Author = {Robin Milner and Joachim Parrow and David Walker},
Date-Added = {2016-12-23 19:10:50 +0000},
Date-Modified = {2016-12-23 19:10:50 +0000},
Doi = {http://dx.doi.org/10.1016/0890-5401(92)90008-4},
Issn = {0890-5401},
Journal = {Information and Computation},
Number = {1},
Pages = {1 - 40},
Title = {A calculus of mobile processes, I},
Url = {http://www.sciencedirect.com/science/article/pii/0890540192900084},
Volume = {100},
Year = {1992},
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Bdsk-Url-2 = {http://dx.doi.org/10.1016/0890-5401(92)90008-4}}
@article{Howard2016Application-of-,
Abstract = {Motivated by their necessity for most fault-tolerant quantum computation schemes, we formulate a resource theory for magic states. We first show that robustness of magic is a well-behaved magic monotone that operationally quantifies the classical simulation overhead for a Gottesman-Knill type scheme using ancillary magic states. Our framework subsequently finds immediate application in the task of synthesizing non-Clifford gates using magic states. When magic states are interspersed with Clifford gates, Pauli measurements and stabilizer ancillas - the most general synthesis scenario - then the class of synthesizable unitaries is hard to characterize. Our techniques can place non-trivial lower bounds on the number of magic states required for implementing a given target unitary. Guided by these results we have found new and optimal examples of such synthesis.},
Author = {Mark Howard and Earl T. Campbell},
Citation_Arxiv_Id = {1609.07488},
Citation_Author = {Campbell, Earl T.},
Citation_Date = {2016/09/23},
Citation_Online_Date = {2016/09/23},
Citation_Pdf_Url = {http://arxiv.org/pdf/1609.07488},
Citation_Title = {Application of a resource theory for magic states to fault-tolerant quantum computing},
Date-Added = {2016-11-07 15:58:09 +0000},
Date-Modified = {2016-11-07 15:58:09 +0000},
Eprint = {arXiv:1609.07488},
Journal = {arXiv.org},
Number = {arXiv:1609.07488},
Title = {Application of a resource theory for magic states to fault-tolerant quantum computing},
Year = {2016},
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@article{Campbell2016Unifying-gate-s,
Abstract = {The leading paradigm for performing computation on quantum memories can be encapsulated as distill-then-synthesize. Initially, one performs several rounds of distillation to create high-fidelity magic states that provide one good T-gate, an essential quantum logic gate. Subsequently, gate synthesis intersperses many T-gates with Clifford gates to realise a desired circuit. We introduce a unified framework that implements one round of distillation and multi-qubit gate synthesis in a single step. Typically, our method uses the same number of T-gates as conventional synthesis, but with the added benefit of quadratic error suppression. Because of this, one less round of magic state distillation needs to be performed, leading to significant resource savings.},
Author = {Earl T. Campbell and Mark Howard},
Citation_Arxiv_Id = {1606.01906},
Citation_Author = {Howard, Mark},
Citation_Date = {2016/06/06},
Citation_Online_Date = {2016/06/06},
Citation_Pdf_Url = {http://arxiv.org/pdf/1606.01906},
Citation_Title = {Unifying gate-synthesis and magic state distillation},
Date-Added = {2016-11-07 15:56:47 +0000},
Date-Modified = {2016-11-07 15:56:47 +0000},
Eprint = {arXiv:1606.01906},
Journal = {arXiv.org},
Number = {arXiv:1606.01906},
Title = {Unifying gate-synthesis and magic state distillation},
Year = {2016},
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@article{Campbell2016A-unified-frame,
Abstract = {The standard approach to fault-tolerant quantum computation is to store information in a quantum error correction code, such as the surface code, and process information using a strategy that can be summarized as distill-then-synthesize. In the distill step, one performs several rounds of distillation to create high-fidelity logical qubits in a magic state. Each such magic state provides one good TT gate. In the synthesize step, one seeks the optimal decomposition of an algorithm into a sequence of many TT gates interleaved with Clifford gates. This gate-synthesis problem is well understood for multi-qubit gates that do not use any Hadamards. We present an in-depth analysis of a unified framework that realises one round of distillation and multi-qubit gate synthesis in a single step. We call these synthillation protocols, and show they lead to a large reduction in resource overheads. This is because synthillation can implement a general class of circuits using the same number of TT-states as gate synthesis, yet with the benefit of quadratic error suppression. Therefore, synthillation removes the need for a costly round of magic state distillation. We also present several additional results on the multi-qubit gate-synthesis problem. We provide an efficient algorithm for synthesising unitaries with the same worst-case resource scaling as optimal solutions. For the special case of synthesizing controlled-unitaries, our techniques are not just efficient but exactly optimal. We observe that the gate-synthesis cost, measured by TT-count, is often strictly subadditive. Numerous explicit applications of our techniques are also presented.},
Author = {Earl T. Campbell and Mark Howard},
Citation_Arxiv_Id = {1606.01904},
Citation_Author = {Howard, Mark},
Citation_Date = {2016/06/06},
Citation_Online_Date = {2016/06/06},
Citation_Pdf_Url = {http://arxiv.org/pdf/1606.01904},
Citation_Title = {A unified framework for magic state distillation and multi-qubit gate-synthesis with reduced resource cost},
Date-Added = {2016-11-07 15:55:06 +0000},
Date-Modified = {2016-11-07 15:55:06 +0000},
Eprint = {arXiv:1606.01904},
Journal = {arXiv.org},
Title = {A unified framework for magic state distillation and multi-qubit gate-synthesis with reduced resource cost},
Volume = {arXiv:1606.01904},
Year = {2016},
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@article{Giles2013Remarks-on-Mats,
Abstract = {Matsumoto and Amano (2008) showed that every single-qubit Clifford+T operator can be uniquely written of a particular form, which we call the Matsumoto-Amano normal form. In this mostly expository paper, we give a detailed and streamlined presentation of Matsumoto and Amano's results, simplifying some proofs along the way. We also point out some corollaries to Matsumoto and Amano's work, including an intrinsic characterization of the Clifford+T subgroup of SO(3), which also yields an efficient T-optimal exact single-qubit synthesis algorithm. Interestingly, this also gives an alternative proof of Kliuchnikov, Maslov, and Mosca's exact synthesis result for the Clifford+T subgroup of U(2).},
Author = {Brett Giles and Peter Selinger},
Citation_Arxiv_Id = {1312.6584},
Citation_Author = {Selinger, Peter},
Citation_Date = {2013/12/23},
Citation_Online_Date = {2013/12/23},
Citation_Pdf_Url = {http://arxiv.org/pdf/1312.6584},
Citation_Title = {Remarks on Matsumoto and Amano's normal form for single-qubit Clifford+T operators},
Date-Added = {2016-11-07 15:52:15 +0000},
Date-Modified = {2016-11-07 15:52:15 +0000},
Eprint = {arXiv:1312.6584},
Journal = {arXiv.org},
Number = {arXiv:1312.6584},
Title = {Remarks on Matsumoto and Amano's normal form for single-qubit Clifford+T operators},
Year = {2013},
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@article{PhysRevA.87.042302,
Author = {Selinger, Peter},
Date-Added = {2016-11-07 15:49:28 +0000},
Date-Modified = {2016-11-07 15:49:53 +0000},
Doi = {10.1103/PhysRevA.87.042302},
Eprint = {https://arxiv.org/abs/1210.0974},
Issue = {4},
Journal = {Phys. Rev. A},
Month = {Apr},
Numpages = {4},
Pages = {042302},
Publisher = {American Physical Society},
Title = {Quantum circuits of $T$-depth one},
Url = {http://link.aps.org/doi/10.1103/PhysRevA.87.042302},
Volume = {87},
Year = {2013},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevA.87.042302},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevA.87.042302}}
@article{Ross2014Optimal-ancilla,
Abstract = {We consider the problem of approximating arbitrary single-qubit z-rotations by ancilla-free Clifford+T circuits, up to given epsilon. We present a fast new probabilistic algorithm for solving this problem optimally, i.e., for finding the shortest possible circuit whatsoever for the given problem instance. The algorithm requires a factoring oracle (such as a quantum computer). Even in the absence of a factoring oracle, the algorithm is still near-optimal under a mild number-theoretic hypothesis. In this case, the algorithm finds a solution of T-count m + O(log(log(1/epsilon))), where m is the T-count of the second-to-optimal solution. In the typical case, this yields circuit approximations of T-count 3log_2(1/epsilon) + O(log(log(1/epsilon))). Our algorithm is efficient in practice, and provably efficient under the above-mentioned number-theoretic hypothesis, in the sense that its expected runtime is O(polylog(1/epsilon)).},
Author = {Neil J. Ross and Peter Selinger},
Citation_Arxiv_Id = {1403.2975},
Citation_Author = {Selinger, Peter},
Citation_Date = {2014/03/12},
Citation_Online_Date = {2016/06/15},
Citation_Pdf_Url = {http://arxiv.org/pdf/1403.2975},
Citation_Title = {Optimal ancilla-free Clifford+T approximation of z-rotations},
Date-Added = {2016-11-07 15:47:26 +0000},
Date-Modified = {2016-11-07 15:47:26 +0000},
Eprint = {arXiv:1403.2975},
Journal = {arXiv.org},
Number = {arXiv:1403.2975},
Title = {Optimal ancilla-free Clifford+T approximation of z-rotations},
Year = {2014},
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@inproceedings{Selinger2016A-finite-altern,
Abstract = {We say that a reversible boolean function on n bits has alternation depth d if it can be written as the sequential composition of d reversible boolean functions, each of which acts only on the top n-1 bits or on the bottom n-1 bits. We show that every reversible boolean function of n >= 4 bits has alternation depth 9.},
Author = {Peter Selinger},
Booktitle = {Reversible Computation 2016},
Citation_Arxiv_Id = {1604.02549},
Citation_Author = {Selinger, Peter},
Citation_Date = {2016/04/09},
Citation_Online_Date = {2016/04/09},
Citation_Pdf_Url = {http://arxiv.org/pdf/1604.02549},
Citation_Title = {A finite alternation result for reversible boolean circuits},
Date-Added = {2016-11-07 15:45:10 +0000},
Date-Modified = {2016-11-07 15:45:10 +0000},
Eprint = {arXiv:1604.02549},
Title = {A finite alternation result for reversible boolean circuits},
Year = {2016},
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@article{Smith2014Quipper:-Concre,
Abstract = {Despite the rich literature on quantum algorithms, there is a surprisingly small amount of coverage of their concrete logical design and implementation. Most resource estimation is done at the level of complexity analysis, but actual concrete numbers (of quantum gates, qubits, etc.) can differ by orders of magnitude. The line of work we present here is a formal framework to write, and reason about, quantum algorithms. Specifically, we designed a language, Quipper, with scalability in mind, and we are able to report actual resource counts for seven non-trivial algorithms found in the quantum computer science literature.},
Author = {Jonathan M. Smith and Neil J. Ross and Peter Selinger and Beno{\^\i}t Valiron},
Citation_Arxiv_Id = {1412.0625},
Citation_Author = {Valiron, Beno{\^\i}t},
Citation_Date = {2014/12/01},
Citation_Online_Date = {2014/12/01},
Citation_Pdf_Url = {http://arxiv.org/pdf/1412.0625},
Citation_Title = {Quipper: Concrete Resource Estimation in Quantum Algorithms},
Date-Added = {2016-11-07 15:42:38 +0000},
Date-Modified = {2016-11-07 15:42:38 +0000},
Eprint = {arXiv:1412.0625},
Journal = {arXiv.org},
Number = {arXiv:1412.0625},
Title = {Quipper: Concrete Resource Estimation in Quantum Algorithms},
Year = {2014},
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@article{Cho2015An-Introduction,
Abstract = {Effectus theory is a new branch of categorical logic that aims to capture the essentials of quantum logic, with probabilistic and Boolean logic as special cases. Predicates in effectus theory are not subobjects having a Heyting algebra structure, like in topos theory, but `characteristic' functions, forming effect algebras. Such effect algebras are algebraic models of quantitative logic, in which double negation holds. Effects in quantum theory and fuzzy predicates in probability theory form examples of effect algebras. This text is an account of the basics of effectus theory. It includes the fundamental duality between states and effects, with the associated Born rule for validity of an effect (predicate) in a particular state. A basic result says that effectuses can be described equivalently in both `total' and `partial' form. So-called `commutative' and `Boolean' effectuses are distinguished, for probabilistic and classical models. It is shown how these Boolean effectuses are essentially extensive categories. A large part of the theory is devoted to the logical notions of comprehension and quotient, which are described abstractly as right adjoint to truth, and as left adjoint to falisity, respectively. It is illustrated how comprehension and quotients are closely related to measurement. The paper closes with a section on `non-commutative' effectus theory, where the appropriate formalisation is not entirely clear yet.},
Author = {Kenta Cho and Bart Jacobs and Bas Westerbaan and Abraham Westerbaan},
Citation_Arxiv_Id = {1512.05813},
Citation_Author = {Westerbaan, Abraham},
Citation_Date = {2015/12/17},
Citation_Online_Date = {2015/12/17},
Citation_Pdf_Url = {http://arxiv.org/pdf/1512.05813},
Citation_Title = {An Introduction to Effectus Theory},
Date-Added = {2016-10-26 12:51:56 +0000},
Date-Modified = {2016-10-26 12:51:56 +0000},
Eprint = {arXiv:1512.05813},
Journal = {arXiv preprint},
Title = {An Introduction to Effectus Theory},
Year = {2015},
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@inproceedings{jacobs:LIPIcs:2015:5530,
Address = {Dagstuhl, Germany},
Annote = {Keywords: Duality, predicate transformer, state transformer, state-and-effect triangle},
Author = {Bart Jacobs},
Booktitle = {6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)},
Date-Added = {2016-10-26 12:44:00 +0000},
Date-Modified = {2016-10-26 12:44:00 +0000},
Doi = {http://dx.doi.org/10.4230/LIPIcs.CALCO.2015.116},
Editor = {Lawrence S. Moss and Pawel Sobocinski},
Isbn = {978-3-939897-84-2},
Issn = {1868-8969},
Pages = {116--129},
Publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
Series = {Leibniz International Proceedings in Informatics (LIPIcs)},
Title = {{A Recipe for State-and-Effect Triangles}},
Url = {http://drops.dagstuhl.de/opus/volltexte/2015/5530},
Urn = {urn:nbn:de:0030-drops-55301},
Volume = {35},
Year = {2015},
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Bdsk-Url-1 = {http://drops.dagstuhl.de/opus/volltexte/2015/5530},
Bdsk-Url-2 = {http://dx.doi.org/10.4230/LIPIcs.CALCO.2015.116}}
@inproceedings{Perdrix:2015aa,
Address = {Dagstuhl, Germany},
Annote = {Keywords: quantum diagram reasoning, completeness, ZX-calculus, quantum computing, categorical quantum mechanics},
Author = {Simon Perdrix and Quanlong Wang},
Booktitle = {41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
Date-Added = {2016-10-21 01:25:46 +0000},
Date-Modified = {2016-10-21 01:29:12 +0000},
Doi = {http://dx.doi.org/10.4230/LIPIcs.MFCS.2016.76},
Editor = {Piotr Faliszewski and Anca Muscholl and Rolf Niedermeier},
Eprint = {arXiv:1506.03055},
Isbn = {978-3-95977-016-3},
Issn = {1868-8969},
Pages = {76:1--76:14},
Publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
Series = {Leibniz International Proceedings in Informatics (LIPIcs)},
Title = {{Supplementarity is Necessary for Quantum Diagram Reasoning}},
Url = {http://drops.dagstuhl.de/opus/volltexte/2016/6506},
Urn = {urn:nbn:de:0030-drops-65062},
Volume = {58},
Year = {2016},
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Bdsk-Url-1 = {http://drops.dagstuhl.de/opus/volltexte/2016/6506},
Bdsk-Url-2 = {http://dx.doi.org/10.4230/LIPIcs.MFCS.2016.76}}
@inproceedings{Backens2016A-Simplified-St,
Author = {Miriam Backens and Simon Perdrix and Quanlong Wang},
Booktitle = {Proceedings of QPL 2016},
Date-Added = {2016-10-21 01:19:48 +0000},
Date-Modified = {2016-10-21 01:24:14 +0000},
Editor = {R. Duncan and C. Heunen},
Eprint = {arXiv:1602.04744},
Note = {to appear},
Series = {EPTCS},
Title = {A Simplified Stabilizer ZX-calculus},
Year = {2016},
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@inproceedings{Chlipala2011Mostly-Automate,
Abstract = {Several recent projects have shown the feasibility of verifying low-level systems software. Verifications based on automated theorem-proving have omitted reasoning about first-class code pointers, which is critical for tasks like certifying implementations of threads and processes. Conversely, verifications that deal with first-class code pointers have featured long, complex, manual proofs. In this paper, we introduce the Bedrock framework, which supports mostly-automated proofs about programs with the full range of features needed to implement, e.g., language runtime systems. The heart of our approach is in mostly-automated discharge of verification conditions inspired by separation logic. Our take on separation logic is computational, in the sense that function specifications are usually written in terms of reference implementations in a purely functional language. Logical quantifiers are the most challenging feature for most automated verifiers; by relying on functional programs (written in the expressive language of the Coq proof assistant), we are able to avoid quantifiers almost entirely. This leads to some dramatic improvements compared to both the state of the art in classical verification, which we compare against with implementations of data structures like binary search trees and hash tables; and the state of the art in verified programming with code pointers, which we compare against with examples like function memoization and a cooperative threading library.},
Author = {Adam Chlipala},
Booktitle = {Proceedings of the ACM SIGPLAN 2011 Conference on Programming Language Design and Implementation (PLDI'11)},
Date-Added = {2016-10-20 23:42:46 +0000},
Date-Modified = {2016-10-20 23:42:46 +0000},
Title = {Mostly-Automated Verification of Low-Level Programs in Computational Separation Logic},
Year = {2011},
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@article{PhysRevA.93.052304,
Author = {Liu, Nana and Thompson, Jayne and Weedbrook, Christian and Lloyd, Seth and Vedral, Vlatko and Gu, Mile and Modi, Kavan},
Date-Added = {2016-10-20 10:45:17 +0000},
Date-Modified = {2016-10-20 10:46:11 +0000},
Doi = {10.1103/PhysRevA.93.052304},
Eprint = {arXiv:1510.04758},
Issue = {5},
Journal = {Phys. Rev. A},
Month = {May},
Numpages = {10},
Pages = {052304},
Publisher = {American Physical Society},
Title = {Power of one qumode for quantum computation},
Url = {http://link.aps.org/doi/10.1103/PhysRevA.93.052304},
Volume = {93},
Year = {2016},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevA.93.052304},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevA.93.052304}}
@article{kelly1980unified,
Author = {Kelly, G. M.},
Date-Added = {2016-10-12 14:43:08 +0000},
Date-Modified = {2016-11-24 12:46:32 +0000},
Doi = {10.1017/S0004972700006353},
Journal = {Bulletin of the Australian Mathematical Society},
Number = {01},
Pages = {1--83},
Publisher = {Cambridge Univ Press},
Title = {A unified treatment of transfinite constructions for free algebras, free monoids, colimits, associated sheaves, and so on},
Volume = {22},
Year = {1980},
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Bdsk-Url-1 = {http://dx.doi.org/10.1017/S0004972700006353}}
@article{PhysRevA.88.012319,
Author = {Dias da Silva, Raphael and Galv\~ao, Ernesto F.},
Date-Added = {2016-10-05 16:02:16 +0000},
Date-Modified = {2016-10-05 16:02:49 +0000},
Doi = {10.1103/PhysRevA.88.012319},
Eprint = {arXiv:1209.5079},
Issue = {1},
Journal = {Phys. Rev. A},
Month = {Jul},
Numpages = {9},
Pages = {012319},
Publisher = {American Physical Society},
Title = {Compact quantum circuits from one-way quantum computation},
Url = {http://link.aps.org/doi/10.1103/PhysRevA.88.012319},
Volume = {88},
Year = {2013},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevA.88.012319},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevA.88.012319}}
@article{Pius:2015:OIF:2871422.2871428,
Address = {Paramus, NJ},
Author = {Pius, Einar and Da Silva, Raphael Dias and Kashefi, Elham},
Date-Added = {2016-10-05 15:58:03 +0000},
Date-Modified = {2016-10-05 16:00:09 +0000},
Issn = {1533-7146},
Journal = {Quantum Info. Comput.},
Keywords = {flow and determinism, measurement-based computing, parallelism},
Month = jul,
Number = {9-10},
Pages = {853--884},
Publisher = {Rinton Press, Incorporated},
Title = {Optimising the Information Flow of One-way Quantum Computations},
Url = {http://dl.acm.org/citation.cfm?id=2871422.2871428},
Volume = {15},
Year = {2015},
Bdsk-Url-1 = {http://dl.acm.org/citation.cfm?id=2871422.2871428}}
@article{Silva2013Global-Quantum-,
Abstract = {One of the main goals in quantum circuit optimisation is to reduce the number of ancillary qubits and the depth of computation, to obtain robust computation. However, most of known techniques, based on local rewriting rules, for parallelising quantum circuits will require the addition of ancilla qubits, leading to an undesired space-time tradeoff. Recently several novel approaches based on measurement-based quantum computation (MBQC) techniques attempted to resolve this problem. The key element is to explore the global structure of a given circuit, defined via translation into a corresponding MBQC pattern. It is known that the parallel power of MBQC is superior to the quantum circuit model, and hence in these approaches one could apply the MBQC depth optimisation techniques to achieve a lower depth. However, currently, once the obtained parallel pattern is translated back to a quantum circuit, one should either increase the depth or add ancilla qubits. In this paper we characterise those computations where both optimisation could be achieved together. In doing so we present a new connection between two MBQC depth optimisation procedures, known as the maximally delayed generalised flow and signal shifting. This structural link will allow us to apply an MBQC qubit optimisation procedure known as compactification to a large class of pattern including all those obtained from any arbitrary quantum circuit. We also present a more efficient algorithm (compared to the existing one) for finding the maximally delayed generalised flow for graph states with flow.},
Author = {Raphael Dias da Silva and Einar Pius and Elham Kashefi},
Citation_Arxiv_Id = {1301.0351},
Citation_Author = {Kashefi, Elham},
Citation_Date = {2013/01/02},
Citation_Online_Date = {2013/01/02},
Citation_Pdf_Url = {http://arxiv.org/pdf/1301.0351},
Citation_Title = {Global Quantum Circuit Optimization},
Date-Added = {2016-10-05 15:54:39 +0000},
Date-Modified = {2016-10-05 15:54:39 +0000},
Eprint = {arXiv:1301.0351},
Journal = {arXiv.org},
Number = {1301.0351},
Title = {Global Quantum Circuit Optimization},
Year = {2013},
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@inproceedings{debeaudrap_et_al:LIPIcs:2014:4818,
Address = {Dagstuhl, Germany},
Annote = {Keywords: Network coding, quantum computing, measurement-based computation, simulation},
Author = {Niel de Beaudrap and Martin Roetteler},
Booktitle = {9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)},
Date-Added = {2016-10-05 15:50:46 +0000},
Date-Modified = {2016-10-05 15:53:38 +0000},
Doi = {10.4230/LIPIcs.TQC.2014.217},
Editor = {Steven T. Flammia and Aram W. Harrow},
Eprint = {arXiv:1403.3533},
Isbn = {978-3-939897-73-6},
Issn = {1868-8969},
Pages = {217--233},
Publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
Series = {Leibniz International Proceedings in Informatics (LIPIcs)},
Title = {{Quantum Linear Network Coding as One-way Quantum Computation}},
Volume = {27},
Year = {2014},
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Bdsk-Url-1 = {http://drops.dagstuhl.de/opus/volltexte/2014/4818},
Bdsk-Url-2 = {http://dx.doi.org/10.4230/LIPIcs.TQC.2014.217}}
@article{Pavlovic2014Monoidal-comput,
Abstract = {In Monoidal Computer I, we introduced a categorical model of computation where the formal reasoning about computability was supported by the simple and popular diagrammatic language of string diagrams. In the present paper, we refine and extend that model of computation to support a formal complexity theory as well. This formalization brings to the foreground the concept of normal complexity measures, which allow decompositions akin to Kleene's normal form. Such measures turn out to be just those where evaluating the complexity of a program does not require substantially more resources than evaluating the program itself. The usual time and space complexity are thus normal measures, whereas the average and the randomized complexity measures are not. While the measures that are not normal provide important design time information about algorithms, and for theoretical analyses, normal measures can also be used at run time, as practical tools of computation, e.g. to set the bounds for hypothesis testing, inductive inference and algorithmic learning.},
Author = {Dusko Pavlovic},
Citation_Arxiv_Id = {1402.5687},
Citation_Author = {Pavlovic, Dusko},
Citation_Date = {2014/02/23},
Citation_Online_Date = {2014/02/23},
Citation_Pdf_Url = {http://arxiv.org/pdf/1402.5687},
Citation_Title = {Monoidal computer II: Normal complexity by string diagrams},
Date-Added = {2016-10-05 15:27:37 +0000},
Date-Modified = {2016-10-05 15:27:37 +0000},
Eprint = {arXiv:1402.5687},
Journal = {arXiv.org},
Number = {1402.5687},
Title = {Monoidal computer II: Normal complexity by string diagrams},
Year = {2014},
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@article{Pavlovic201394,
Abstract = {Abstract We present a new model of computation, described in terms of monoidal categories. It conforms to the Church--Turing Thesis, and captures the same computable functions as the standard models. It provides a succinct categorical interface to most of them, free of their diverse implementation details, using the ideas and structures that in the meantime emerged from research in semantics of computation and programming. The salient feature of the language of monoidal categories is that it is supported by a sound and complete graphical formalism, string diagrams, which provide a concrete and intuitive interface for abstract reasoning about computation. The original motivation and the ultimate goal of this effort is to provide a convenient high level programming language for a theory of computational resources, such as one-way functions, and trapdoor functions, by adopting the methods for hiding the low level implementation details that emerged from practice. },
Author = {Dusko Pavlovic},
Date-Added = {2016-10-05 15:25:24 +0000},
Date-Modified = {2016-10-05 15:25:24 +0000},
Doi = {http://dx.doi.org/10.1016/j.ic.2013.03.007},
Issn = {0890-5401},
Journal = {Information and Computation},
Note = {Special Issue: Information Security as a Resource},
Pages = {94 - 116},
Title = {Monoidal computer I: Basic computability by string diagrams},
Url = {http://www.sciencedirect.com/science/article/pii/S0890540113000254},
Volume = {226},
Year = {2013},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0890540113000254},
Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.ic.2013.03.007}}
@article{childress2013,
Abstract = {The exotic features of quantum mechanics have the potential to revolutionize information technologies. Using superposition and entanglement, a quantum processor could efficiently tackle problems inaccessible to current-day computers. Nonlocal correlations may be exploited for intrinsically secure communication across the globe. Finding and controlling a physical system suitable for fulfilling these promises is one of the greatest challenges of our time. The nitrogen-vacancy (NV) center in diamond has recently emerged as one of the leading candidates for such quantum information technologies thanks to its combination of atom-like properties and solid-state host environment. We review the remarkable progress made in the past years in controlling electrons, atomic nuclei, and light at the single-quantum level in diamond. We also discuss prospects and challenges for the use of NV centers in future quantum technologies.},
Address = {New York, USA},
Author = {Lilian Childress and Ronald Hanson},
Date-Added = {2016-09-30 13:34:15 +0000},
Date-Modified = {2016-09-30 13:34:15 +0000},
Day = {006},
Doi = {10.1557/mrs.2013.20},
Journal = {MRS Bulletin},
Month = {002},
Number = {2},
Pages = {134-138},
Publisher = {Cambridge University Press},
Title = {Diamond NV centers for quantum computing and quantum networks},
Url = {https://www.cambridge.org/core/article/diamond-nv-centers-for-quantum-computing-and-quantum-networks/978A4B94242CF28F9C60F0D9E95E9CBD},
Volume = {38},
Year = {2013},
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Bdsk-Url-1 = {https://www.cambridge.org/core/article/diamond-nv-centers-for-quantum-computing-and-quantum-networks/978A4B94242CF28F9C60F0D9E95E9CBD},
Bdsk-Url-2 = {http://dx.doi.org/10.1557/mrs.2013.20}}
@article{Riste2013Deterministic-e,
Author = {Riste, D. and Dukalski, M. and Watson, C. A. and de Lange, G. and Tiggelman, M. J. and Blanter, Ya. M. and Lehnert, K. W. and Schouten, R. N. and DiCarlo, L.},
Date-Added = {2016-09-30 13:02:55 +0000},
Date-Modified = {2016-09-30 13:03:31 +0000},
Doi = {10.1038/nature12513},
Isbn = {0028-0836},
Journal = {Nature},
Month = {10},
Number = {7471},
Pages = {350--354},
Title = {Deterministic entanglement of superconducting qubits by parity measurement and feedback},
Url = {http://dx.doi.org/10.1038/nature12513},
Volume = {502},
Year = {2013},
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Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature12513}}
@article{DiCarlo2009Demonstration-o,
Annote = {10.1038/nature08121},
Author = {DiCarlo, L. and Chow, J. M. and Gambetta, J. M. and Bishop, Lev S. and Johnson, B. R. and Schuster, D. I. and Majer, J. and Blais, A. and Frunzio, L. and Girvin, S. M. and Schoelkopf, R. J.},
Date-Added = {2016-09-30 12:52:13 +0000},
Date-Modified = {2016-09-30 12:52:37 +0000},
Doi = {10.1038/nature08121},
Isbn = {0028-0836},
Journal = {Nature},
Month = {07},
Number = {7252},
Pages = {240--244},
Title = {Demonstration of two-qubit algorithms with a superconducting quantum processor},
Url = {http://dx.doi.org/10.1038/nature08121},
Volume = {460},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature08121}}
@article{Chiorescu2003Coherent-Quantu,
Author = {I. Chiorescu and Y. Nakamura and C. J. P. M. Harmans and J. E. Mooij},
Date-Added = {2016-09-30 12:41:41 +0000},
Date-Modified = {2016-09-30 12:41:41 +0000},
Doi = {10.1126/science.1081045},
Journal = {Science},
Number = {5614},
Pages = {1869-1871},
Title = {Coherent Quantum Dynamics of a Superconducting Flux Qubit},
Volume = {299},
Year = {2003},
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Bdsk-Url-1 = {http://dx.doi.org/10.1126/science.1081045}}
@inproceedings{William-Zeng-Rigetti-Computing2016Quantum-Algorit,
Abstract = {We propose a new application of quantum computing to the field of natural language processing. Ongoing work in this field attempts to incorporate grammatical structure into algorithms that compute meaning. In (Coecke, Sadrzadeh and Clark, 2010), the authors introduce such a model (the CSC model) based on tensor product composition. While this algorithm has many advantages, its implementation is hampered by the large classical computational resources that it requires. In this work we show how computational shortcomings of the CSC approach could be resolved using quantum computation (possibly in addition to existing techniques for dimension reduction). We address the value of quantum RAM (Giovannetti,2008) for this model and extend an algorithm from Wiebe, Braun and Lloyd (2012) into a quantum algorithm to categorize sentences in CSC. Our new algorithm demonstrates a quadratic speedup over classical methods under certain conditions.},
Author = {William Zeng and Bob Coecke},
Booktitle = {Proceedings SLPCS 2016},
Citation_Arxiv_Id = {1608.01406},
Citation_Author = {Coecke, Bob},
Citation_Date = {2016/08/04},
Citation_Doi = {10.4204/EPTCS.221.8},
Citation_Online_Date = {2016/08/04},
Citation_Pdf_Url = {http://arxiv.org/pdf/1608.01406},
Citation_Title = {Quantum Algorithms for Compositional Natural Language Processing},
Date-Added = {2016-09-30 11:52:08 +0000},
Date-Modified = {2016-09-30 16:10:17 +0000},
Eprint = {arXiv:1608.01406},
Pages = {67-75},
Series = {EPTCS},
Title = {Quantum Algorithms for Compositional Natural Language Processing},
Volume = {221},
Year = {2016},
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@article{fritz2015,
Abstract = {Resources and their use and consumption form a central part of our life. Many branches of science and engineering are concerned with the question of which given resource objects can be converted into which target resource objects. For example, information theory studies the conversion of a noisy communication channel instance into an exchange of information. Inspired by work in quantum information theory, we develop a general mathematical toolbox for this type of question. The convertibility of resources into other ones and the possibility of combining resources is accurately captured by the mathematics of ordered commutative monoids. As an intuitive example, we consider chemistry, where chemical reaction equations such as
\textbackslashmathrm\{2H\_2 + O\_2\} \textbackslashlra \textbackslashmathrm\{2H\_2O,\}
are concerned both with a convertibility relation `→' and a combination operation `+.' We study ordered commutative monoids from an algebraic and functional-analytic perspective },
Address = {Cambridge, UK},
Author = {Tobias Fritz},
Date-Added = {2016-09-30 11:13:47 +0000},
Date-Modified = {2016-09-30 11:14:29 +0000},
Day = {12},
Doi = {10.1017/S0960129515000444},
Eprint = {arXiv:1504.03661},
Journal = {Mathematical Structures in Computer Science},
Month = {10},
Pages = {1-89},
Publisher = {Cambridge University Press},
Title = {Resource convertibility and ordered commutative monoids},
Url = {https://www.cambridge.org/core/article/resource-convertibility-and-ordered-commutative-monoids/C0D57AE7683BAA911F3F270ABD82A4E9},
Year = {2015},
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Bdsk-Url-1 = {https://www.cambridge.org/core/article/resource-convertibility-and-ordered-commutative-monoids/C0D57AE7683BAA911F3F270ABD82A4E9},
Bdsk-Url-2 = {http://dx.doi.org/10.1017/S0960129515000444}}
@inproceedings{DBLP:journals/corr/FongN15,
Author = {Brendan Fong and Hugo Nava{-}Kopp},
Booktitle = {Proceedings 12th International Workshop on Quantum Physics and Logic, {QPL} 2015, Oxford, UK, July 15-17, 2015.},
Date-Added = {2016-09-30 11:11:50 +0000},
Date-Modified = {2017-02-07 22:34:20 +0000},
Doi = {10.4204/EPTCS.195.13},
Pages = {170--178},
Title = {Additive monotones for resource theories of parallel-combinable processes with discarding},
Year = {2015},
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Bdsk-Url-1 = {http://dx.doi.org/10.4204/EPTCS.195.13}}
@article{PhysRevLett.108.120402,
Author = {Boixo, Sergio and Heunen, Chris},
Date-Added = {2016-09-30 03:35:30 +0000},
Date-Modified = {2016-09-30 04:10:49 +0000},
Doi = {10.1103/PhysRevLett.108.120402},
Eprint = {arXiv:1108.3569},
Issue = {12},
Journal = {Phys. Rev. Lett.},
Month = {Mar},
Numpages = {5},
Pages = {120402},
Publisher = {American Physical Society},
Title = {Entangled and Sequential Quantum Protocols with Dephasing},
Url = {http://link.aps.org/doi/10.1103/PhysRevLett.108.120402},
Volume = {108},
Year = {2012},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.108.120402},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.108.120402}}
@article{1367-2630-17-10-103027,
Abstract = {Entanglement is one of the most striking features of quantum mechanics, and yet it is not specifically quantum. More specific to quantum mechanics is the connection between entanglement and thermodynamics, which leads to an identification between entropies and measures of pure state entanglement. Here we search for the roots of this connection, investigating the relation between entanglement and thermodynamics in the framework of general probabilistic theories. We first address the question whether an entangled state can be transformed into another by means of local operations and classical communication. Under two operational requirements, we prove a general version of the Lo--Popescu theorem, which lies at the foundations of the theory of pure-state entanglement. We then consider a resource theory of purity where free operations are random reversible transformations, modelling the scenario where an agent has limited control over the dynamics of a closed system. Our key result is a duality between the resource theory of entanglement and the resource theory of purity, valid for every physical theory where all processes arise from pure states and reversible interactions at the fundamental level. As an application of the main result, we establish a one-to-one correspondence between entropies and measures of pure bipartite entanglement. The correspondence is then used to define entanglement measures in the general probabilistic framework. Finally, we show a duality between the task of information erasure and the task of entanglement generation, whereby the existence of entropy sinks (systems that can absorb arbitrary amounts of information) becomes equivalent to the existence of entanglement sources (correlated systems from which arbitrary amounts of entanglement can be extracted).},
Author = {Giulio Chiribella and Carlo Maria Scandolo},
Date-Added = {2016-09-29 16:07:52 +0000},
Date-Modified = {2016-09-29 16:07:52 +0000},
Journal = {New Journal of Physics},
Number = {10},
Pages = {103027},
Title = {Entanglement and thermodynamics in general probabilistic theories},
Url = {http://stacks.iop.org/1367-2630/17/i=10/a=103027},
Volume = {17},
Year = {2015},
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Bdsk-Url-1 = {http://stacks.iop.org/1367-2630/17/i=10/a=103027}}
@article{Chiribella2016Optimal-quantum,
Abstract = {We develop a semidefinite programming method for the optimization of quantum networks, including both causal networks and networks with indefinite causal structure. Our method applies to a broad class of performance measures, defined operationally in terms of interactive tests set up by a verifier. We show that the optimal performance is equal to a max relative entropy, which quantifies the informativeness of the test. Building on this result, we extend the notion of conditional min-entropy from quantum states to quantum causal networks. The optimization method is illustrated in a number of applications, including the inversion, charge conjugation, and controlization of an unknown unitary dynamics. In the non-causal setting, we show a proof-of-principle application to the maximization of the winning probability in a non-causal quantum game.},
Author = {Giulio Chiribella and Daniel Ebler},
Citation_Arxiv_Id = {1606.02394},
Citation_Author = {Ebler, Daniel},
Citation_Date = {2016/06/08},
Citation_Online_Date = {2016/09/06},
Citation_Pdf_Url = {http://arxiv.org/pdf/1606.02394},
Citation_Title = {Optimal quantum networks and one-shot entropies},
Date-Added = {2016-09-29 16:06:08 +0000},
Date-Modified = {2016-09-29 16:06:08 +0000},
Eprint = {arXiv:1606.02394},
Journal = {New Journal of Physics},
Title = {Optimal quantum networks and one-shot entropies},
Volume = {to appear},
Year = {2016},
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@article{Chiribella2016Purity-in-micro,
Author = {Giulio Chiribella and Carlo Maria Scandolo},
Citation_Arxiv_Id = {1608.04460},
Citation_Author = {Scandolo, Carlo Maria},
Citation_Date = {2016/08/16},
Citation_Online_Date = {2016/08/17},
Citation_Pdf_Url = {http://arxiv.org/pdf/1608.04460},
Citation_Title = {Purity in microcanonical thermodynamics: a tale of three resource theories},
Date-Added = {2016-09-29 16:03:17 +0000},
Date-Modified = {2016-09-29 16:03:17 +0000},
Eprint = {arXiv:1608.04460},
Journal = {arXiv preprint},
Number = {1608.04460},
Title = {Purity in microcanonical thermodynamics: a tale of three resource theories},
Year = {2016},
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@article{chiribella2013quantum,
Author = {Chiribella, Giulio and D'Ariano, Giacomo Mauro and Perinotti, Paolo and Valiron, Benoit},
Date-Added = {2016-09-29 15:57:49 +0000},
Date-Modified = {2016-09-29 16:00:24 +0000},
Eprint = {arXiv:0912.0195},
Journal = {Physical Review A},
Number = {2},
Pages = {022318},
Publisher = {American Physical Society},
Title = {Quantum computations without definite causal structure},
Volume = {88},
Year = {2013},
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@inproceedings{Pirog:2016:SDF:2951913.2951947,
Acmid = {2951947},
Address = {New York, NY, USA},
Author = {Pir\'{o}g, Maciej and Wu, Nicolas},
Booktitle = {Proceedings of the 21st ACM SIGPLAN International Conference on Functional Programming},
Date-Added = {2016-09-29 15:50:12 +0000},
Date-Modified = {2016-09-29 15:50:12 +0000},
Doi = {10.1145/2951913.2951947},
Isbn = {978-1-4503-4219-3},
Keywords = {distributive law, free monad, monad, string diagram, universal property},
Location = {Nara, Japan},
Numpages = {12},
Pages = {490--501},
Publisher = {ACM},
Series = {ICFP 2016},
Title = {String Diagrams for Free Monads (Functional Pearl)},
Url = {http://doi.acm.org/10.1145/2951913.2951947},
Year = {2016},
Bdsk-Url-1 = {http://doi.acm.org/10.1145/2951913.2951947},
Bdsk-Url-2 = {http://dx.doi.org/10.1145/2951913.2951947}}
@article{DBLP:journals/corr/HedgesS16,
Author = {Jules Hedges and Mehrnoosh Sadrzadeh},
Date-Added = {2016-09-29 11:16:20 +0000},
Date-Modified = {2016-09-29 11:16:55 +0000},
Eprint = {arxiv:1602.01635},
Journal = {CoRR},
Title = {A Generalised Quantifier Theory of Natural Language in Categorical Compositional Distributional Semantics with Bialgebras},
Url = {http://arxiv.org/abs/1602.01635},
Volume = {abs/1602.01635},
Year = {2016},
Bdsk-Url-1 = {http://arxiv.org/abs/1602.01635}}
@book{Coecke2017Picturing-Quant,
Author = {Bob Coecke and Aleks Kissinger},
Date-Added = {2016-09-29 10:43:20 +0000},
Date-Modified = {2017-02-23 16:14:48 +0000},
Publisher = {Cambridge University Press},
Title = {Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning},
Year = {2017}}
@article{gerstenhaber1961,
Author = {Gerstenhaber, Murray},
Date-Added = {2016-09-01 15:24:46 +0000},
Date-Modified = {2016-09-01 15:24:46 +0000},
Fjournal = {Illinois Journal of Mathematics},
Journal = {Illinois J. Math.},
Month = {06},
Number = {2},
Pages = {330--333},
Publisher = {University of Illinois at Urbana-Champaign, Department of Mathematics},
Title = {On the number of nilpotent matrices with coefficients in a finite field},
Url = {http://projecteuclid.org/euclid.ijm/1255629831},
Volume = {5},
Year = {1961},
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Bdsk-Url-1 = {http://projecteuclid.org/euclid.ijm/1255629831}}
@article{Jacobs97atutorial,
Author = {Bart Jacobs and Jan Rutten},
Date-Added = {2016-08-15 15:53:20 +0000},
Date-Modified = {2016-08-15 15:53:20 +0000},
Journal = {EATCS Bulletin},
Pages = {62--222},
Title = {A Tutorial on (Co)Algebras and (Co)Induction},
Volume = {62},
Year = {1997},
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@article{PhysRevA.64.012310,
Author = {Gottesman, Daniel and Kitaev, Alexei and Preskill, John},
Date-Added = {2016-08-01 17:09:55 +0000},
Date-Modified = {2016-08-01 17:09:55 +0000},
Doi = {10.1103/PhysRevA.64.012310},
Issue = {1},
Journal = {Phys. Rev. A},
Month = {Jun},
Numpages = {21},
Pages = {012310},
Publisher = {American Physical Society},
Title = {Encoding a qubit in an oscillator},
Url = {http://link.aps.org/doi/10.1103/PhysRevA.64.012310},
Volume = {64},
Year = {2001},
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@article{PhysRevLett.112.120504,
Author = {Menicucci, Nicolas C.},
Date-Added = {2016-08-01 17:08:12 +0000},
Date-Modified = {2016-08-01 17:08:12 +0000},
Doi = {10.1103/PhysRevLett.112.120504},
Issue = {12},
Journal = {Phys. Rev. Lett.},
Month = {Mar},
Numpages = {5},
Pages = {120504},
Publisher = {American Physical Society},
Title = {Fault-Tolerant Measurement-Based Quantum Computing with Continuous-Variable Cluster States},
Url = {http://link.aps.org/doi/10.1103/PhysRevLett.112.120504},
Volume = {112},
Year = {2014},
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@article{PhysRevA.90.062324,
Author = {Alexander, Rafael N. and Armstrong, Seiji C. and Ukai, Ryuji and Menicucci, Nicolas C.},
Date-Added = {2016-08-01 17:07:02 +0000},
Date-Modified = {2016-08-01 17:07:02 +0000},
Doi = {10.1103/PhysRevA.90.062324},
Issue = {6},
Journal = {Phys. Rev. A},
Month = {Dec},
Numpages = {19},
Pages = {062324},
Publisher = {American Physical Society},
Title = {Noise analysis of single-mode Gaussian operations using continuous-variable cluster states},
Url = {http://link.aps.org/doi/10.1103/PhysRevA.90.062324},
Volume = {90},
Year = {2014},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevA.90.062324},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevA.90.062324}}
@article{PhysRevA.79.062318,
Author = {Gu, Mile and Weedbrook, Christian and Menicucci, Nicolas C. and Ralph, Timothy C. and van Loock, Peter},
Date-Added = {2016-08-01 17:06:16 +0000},
Date-Modified = {2016-08-01 17:06:16 +0000},
Doi = {10.1103/PhysRevA.79.062318},
Issue = {6},
Journal = {Phys. Rev. A},
Month = {Jun},
Numpages = {16},
Pages = {062318},
Publisher = {American Physical Society},
Title = {Quantum computing with continuous-variable clusters},
Url = {http://link.aps.org/doi/10.1103/PhysRevA.79.062318},
Volume = {79},
Year = {2009},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevA.79.062318},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevA.79.062318}}
@article{Alexander2015One-way-quantum,
Abstract = {One-way quantum computing is experimentally appealing because it requires only local measurements on an entangled resource called a cluster state. Record-size, but non-universal, continuous-variable cluster states were recently demonstrated separately in the time and frequency domains. We propose to combine these approaches into a scalable architecture in which a single optical parametric oscillator and simple interferometer entangle up to (3×1033\times 10^3 frequencies) ×\times (unlimited number of temporal modes) into a new and computationally universal continuous-variable cluster state. We introduce a generalized measurement protocol to enable improved computational performance on the new entanglement resource.},
Author = {Rafael N. Alexander and Pei Wang and Niranjan Sridhar and Moran Chen and Olivier Pfister and Nicolas C. Menicucci},
Date-Added = {2016-08-01 17:03:28 +0000},
Date-Modified = {2017-02-07 11:13:16 +0000},
Doi = {10.1103/PhysRevA.94.032327},
Eprint = {arXiv:1509.00484},
Journal = {Phys. Rev. A},
Number = {032327},
Title = {One-way quantum computing with arbitrarily large time-frequency continuous-variable cluster states from a single optical parametric oscillator},
Volume = {94},
Year = {2016},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.94.032327}}
@article{PhysRevA.90.032325,
Author = {Wang, Pei and Chen, Moran and Menicucci, Nicolas C. and Pfister, Olivier},
Date-Added = {2016-08-01 17:01:14 +0000},
Date-Modified = {2016-08-01 17:01:14 +0000},
Doi = {10.1103/PhysRevA.90.032325},
Issue = {3},
Journal = {Phys. Rev. A},
Month = {Sep},
Numpages = {8},
Pages = {032325},
Publisher = {American Physical Society},
Title = {Weaving quantum optical frequency combs into continuous-variable hypercubic cluster states},
Url = {http://link.aps.org/doi/10.1103/PhysRevA.90.032325},
Volume = {90},
Year = {2014},
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Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevA.90.032325}}
@article{PhysRevA.83.062314,
Author = {Menicucci, Nicolas C.},
Date-Added = {2016-08-01 17:00:37 +0000},
Date-Modified = {2016-08-01 17:00:37 +0000},
Doi = {10.1103/PhysRevA.83.062314},
Issue = {6},
Journal = {Phys. Rev. A},
Month = {Jun},
Numpages = {9},
Pages = {062314},
Publisher = {American Physical Society},
Title = {Temporal-mode continuous-variable cluster states using linear optics},
Url = {http://link.aps.org/doi/10.1103/PhysRevA.83.062314},
Volume = {83},
Year = {2011},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevA.83.062314},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevA.83.062314}}
@article{PhysRevLett.112.120505,
Author = {Chen, Moran and Menicucci, Nicolas C. and Pfister, Olivier},
Date-Added = {2016-08-01 16:59:41 +0000},
Date-Modified = {2016-08-01 16:59:41 +0000},
Doi = {10.1103/PhysRevLett.112.120505},
Issue = {12},
Journal = {Phys. Rev. Lett.},
Month = {Mar},
Numpages = {5},
Pages = {120505},
Publisher = {American Physical Society},
Title = {Experimental Realization of Multipartite Entanglement of 60 Modes of a Quantum Optical Frequency Comb},
Url = {http://link.aps.org/doi/10.1103/PhysRevLett.112.120505},
Volume = {112},
Year = {2014},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.112.120505},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.112.120505}}
@article{Yokoyama2013Ultra-large-sca,
Abstract = {Quantum computers promise ultrafast performance for certain tasks. Experimentally appealing, measurement-based quantum computation requires an entangled resource called a cluster state, with long computations requiring large cluster states. Previously, the largest cluster state consisted of eight photonic qubits or light modes, and the largest multipartite entangled state of any sort involved 14 trapped ions. These implementations involve quantum entities separated in space and, in general, each experimental apparatus is used only once. Here, we circumvent this inherent inefficiency by multiplexing light modes in the time domain. We deterministically generate and fully characterize a continuous-variable cluster state containing more than 10,000 entangled modes. This is, by three orders of magnitude, the largest entangled state created to date. The entangled modes are individually addressable wave packets of light in two beams. Furthermore, we present an efficient scheme for measurement-based quantum computation on this cluster state based on sequential applications of quantum teleportation.},
Author = {Yokoyama, Shota and Ukai, Ryuji and Armstrong, Seiji C. and Sornphiphatphong, Chanond and Kaji, Toshiyuki and Suzuki, Shigenari and Yoshikawa, Jun-ichi and Yonezawa, Hidehiro and Menicucci, Nicolas C. and Furusawa, Akira},
Date-Added = {2016-08-01 16:58:04 +0000},
Date-Modified = {2016-08-01 16:58:30 +0000},
Doi = {10.1038/nphoton.2013.287},
Journal = {Nat Photon},
Month = {12},
Number = {12},
Pages = {982--986},
Title = {Ultra-large-scale continuous-variable cluster states multiplexed in the time domain},
Url = {http://dx.doi.org/10.1038/nphoton.2013.287},
Volume = {7},
Year = {2013},
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Bdsk-Url-1 = {http://dx.doi.org/10.1038/nphoton.2013.287}}
@article{PhysRevA.86.032120,
Author = {Raimond, J. M. and Facchi, P. and Peaudecerf, B. and Pascazio, S. and Sayrin, C. and Dotsenko, I. and Gleyzes, S. and Brune, M. and Haroche, S.},
Date-Added = {2016-08-01 16:56:46 +0000},
Date-Modified = {2016-08-01 16:56:46 +0000},
Doi = {10.1103/PhysRevA.86.032120},
Issue = {3},
Journal = {Phys. Rev. A},
Month = {Sep},
Numpages = {15},
Pages = {032120},
Publisher = {American Physical Society},
Title = {Quantum Zeno dynamics of a field in a cavity},
Url = {http://link.aps.org/doi/10.1103/PhysRevA.86.032120},
Volume = {86},
Year = {2012},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevA.86.032120},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevA.86.032120}}
@article{1367-2630-16-4-045011,
Abstract = {We describe the creation of nonclassical states of microwave radiation via ideal dichotomic single photon detection, i.e., a detector that only indicates presence or absence of photons. Ideally, such a detector has a back action in the form of the subtraction operator (bare lowering operator). Using the non-linearity of this back action, it is possible to create a large family of nonclassical states of microwave radiation, including squeezed and multi-component cat states, starting from a coherent state. We discuss the applicability of this protocol to current experimental designs of Josephson photomultipliers.},
Author = {Luke C G Govia and Emily J Pritchett and Frank K Wilhelm},
Date-Added = {2016-08-01 16:54:43 +0000},
Date-Modified = {2016-08-01 16:54:43 +0000},
Journal = {New Journal of Physics},
Number = {4},
Pages = {045011},
Title = {Generating nonclassical states from classical radiation by subtraction measurements},
Url = {http://stacks.iop.org/1367-2630/16/i=4/a=045011},
Volume = {16},
Year = {2014},
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Bdsk-Url-1 = {http://stacks.iop.org/1367-2630/16/i=4/a=045011}}
@article{1367-2630-18-2-023028,
Abstract = {Perfect deterministic amplification of arbitrary quantum states is prohibited by quantum mechanics, but determinism can be achieved by compromising between fidelity and amplification power. We propose a dynamical scheme for deterministically amplifying photonic Schr{\"o}dinger cat states, which show great promise as a tool for quantum information processing. Our protocol is designed for strongly coupled circuit quantum electrodynamics and utilizes artificial atomic states and external microwave controls to engineer a set of optimal state transfers and achieve high fidelity amplification. We compare analytical results with full simulations of the open, driven Jaynes--Cummings model, using realistic device parameters for state of the art superconducting circuits. Amplification with a fidelity of 0.9 can be achieved for sizable cat states in the presence of cavity and atomic-level decoherence. This tool could be applied to practical continuous-variable information processing for the purification and stabilization of cat states in the presence of photon losses.},
Author = {Jaewoo Joo and Matthew Elliott and Daniel K L Oi and Eran Ginossar and Timothy P Spiller},
Date-Added = {2016-08-01 16:53:07 +0000},
Date-Modified = {2016-08-01 16:53:07 +0000},
Journal = {New Journal of Physics},
Number = {2},
Pages = {023028},
Title = {Deterministic amplification of Schr{\"o}dinger cat states in circuit quantum electrodynamics},
Url = {http://stacks.iop.org/1367-2630/18/i=2/a=023028},
Volume = {18},
Year = {2016},
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Bdsk-Url-1 = {http://stacks.iop.org/1367-2630/18/i=2/a=023028}}
@article{Um2016Phonon-arithmet,
Abstract = {Single-quantum level operations are important tools to manipulate a quantum state. Annihilation or creation of single particles translates a quantum state to another by adding or subtracting a particle, depending on how many are already in the given state. The operations are probabilistic and the success rate has yet been low in their experimental realization. Here we experimentally demonstrate (near) deterministic addition and subtraction of a bosonic particle, in particular a phonon of ionic motion in a harmonic potential. We realize the operations by coupling phonons to an auxiliary two-level system and applying transitionless adiabatic passage. We show handy repetition of the operations on various initial states and demonstrate by the reconstruction of the density matrices that the operations preserve coherences. We observe the transformation of a classical state to a highly non-classical one and a Gaussian state to a non-Gaussian one by applying a sequence of operations deterministically.},
Author = {Um, Mark and Zhang, Junhua and Lv, Dingshun and Lu, Yao and An, Shuoming and Zhang, Jing-Ning and Nha, Hyunchul and Kim, M. S. and Kim, Kihwan},
Date-Added = {2016-08-01 16:51:38 +0000},
Date-Modified = {2016-08-01 16:52:08 +0000},
Doi = {10.1038/ncomms11410},
Journal = {Nat Commun},
Month = {04},
Title = {Phonon arithmetic in a trapped ion system},
Url = {http://dx.doi.org/10.1038/ncomms11410},
Volume = {7},
Year = {2016},
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Bdsk-Url-1 = {http://dx.doi.org/10.1038/ncomms11410}}
@book{Ewald2013David-Hilberts-,
Author = {William Ewald and Wilfried Sieg},
Date-Added = {2016-08-01 16:49:27 +0000},
Date-Modified = {2016-08-01 16:50:41 +0000},
Publisher = {Springer-Verlag},
Title = {David Hilbert's Lectures on the Foundations of Arithmetic and Logic 1917-1933},
Year = {2013}}
@book{gamow1947one,
Author = {Gamow, G.},
Date-Added = {2016-08-01 16:46:08 +0000},
Date-Modified = {2016-08-01 16:47:45 +0000},
Publisher = {Viking Press},
Title = {One Two Three . . . Infinity: Facts and Speculations of Science},
Year = {1947},
Bdsk-Url-1 = {https://books.google.co.uk/books?id=fu-SjQudB%5C_0C}}
@article{Parigi1890,
Abstract = {The possibility of arbitrarily {\textquotedblleft}adding{\textquotedblright} and {\textquotedblleft}subtracting{\textquotedblright} single photons to and from a light field may give access to a complete engineering of quantum states and to fundamental quantum phenomena. We experimentally implemented simple alternated sequences of photon creation and annihilation on a thermal field and used quantum tomography to verify the peculiar character of the resulting light states. In particular, as the final states depend on the order in which the two actions are performed, we directly observed the noncommutativity of the creation and annihilation operators, one of the cardinal concepts of quantum mechanics, at the basis of the quantum behavior of light. These results represent a step toward the full quantum control of a field and may provide new resources for quantum information protocols.},
Author = {Parigi, Valentina and Zavatta, Alessandro and Kim, Myungshik and Bellini, Marco},
Date-Added = {2016-08-01 16:44:12 +0000},
Date-Modified = {2016-08-01 16:44:12 +0000},
Doi = {10.1126/science.1146204},
Eprint = {http://science.sciencemag.org/content/317/5846/1890.full.pdf},
Issn = {0036-8075},
Journal = {Science},
Number = {5846},
Pages = {1890--1893},
Publisher = {American Association for the Advancement of Science},
Title = {Probing Quantum Commutation Rules by Addition and Subtraction of Single Photons to/from a Light Field},
Url = {http://science.sciencemag.org/content/317/5846/1890},
Volume = {317},
Year = {2007},
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Bdsk-Url-1 = {http://science.sciencemag.org/content/317/5846/1890},
Bdsk-Url-2 = {http://dx.doi.org/10.1126/science.1146204}}
@article{Ourjoumtsev83,
Abstract = {We present a detailed experimental analysis of a free-propagating light pulse prepared in a {\textquotedblleft}Schr{\"o}dinger kitten{\textquotedblright} state, which is defined as a quantum superposition of {\textquotedblleft}classical{\textquotedblright} coherent states with small amplitudes. This kitten state is generated by subtracting one photon from a squeezed vacuum beam, and it clearly presents a negative Wigner function. The predicted influence of the experimental parameters is in excellent agreement with the experimental results. The amplitude of the coherent states can be amplified to transform our {\textquotedblleft}Schr{\"o}dinger kittens{\textquotedblright} into bigger Schr{\"o}dinger cats, providing an essential tool for quantum information processing.},
Author = {Ourjoumtsev, Alexei and Tualle-Brouri, Rosa and Laurat, Julien and Grangier, Philippe},
Date-Added = {2016-08-01 16:43:04 +0000},
Date-Modified = {2016-08-01 16:43:04 +0000},
Doi = {10.1126/science.1122858},
Eprint = {http://science.sciencemag.org/content/312/5770/83.full.pdf},
Issn = {0036-8075},
Journal = {Science},
Number = {5770},
Pages = {83--86},
Publisher = {American Association for the Advancement of Science},
Title = {Generating Optical Schr{\"o}dinger Kittens for Quantum Information Processing},
Url = {http://science.sciencemag.org/content/312/5770/83},
Volume = {312},
Year = {2006},
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Bdsk-Url-1 = {http://science.sciencemag.org/content/312/5770/83},
Bdsk-Url-2 = {http://dx.doi.org/10.1126/science.1122858}}
@article{Zavatta660,
Abstract = {Single-photon{\textendash}added coherent states are the result of the most elementary amplification process of classical light fields by a single quantum of excitation. Being intermediate between a single-photon Fock state (fully quantum-mechanical) and a coherent (classical) one, these states offer the opportunity to closely follow the smooth transition between the particle-like and the wavelike behavior of light. We report the experimental generation of single-photon{\textendash}added coherent states and their complete characterization by quantum tomography. Besides visualizing the evolution of the quantum-to-classical transition, these states allow one to witness the gradual change from the spontaneous to the stimulated regimes of light emission.},
Author = {Zavatta, Alessandro and Viciani, Silvia and Bellini, Marco},
Date-Added = {2016-08-01 16:41:32 +0000},
Date-Modified = {2016-08-01 16:41:32 +0000},
Doi = {10.1126/science.1103190},
Eprint = {http://science.sciencemag.org/content/306/5696/660.full.pdf},
Issn = {0036-8075},
Journal = {Science},
Number = {5696},
Pages = {660--662},
Publisher = {American Association for the Advancement of Science},
Title = {Quantum-to-Classical Transition with Single-Photon-Added Coherent States of Light},
Url = {http://science.sciencemag.org/content/306/5696/660},
Volume = {306},
Year = {2004},
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Bdsk-Url-1 = {http://science.sciencemag.org/content/306/5696/660},
Bdsk-Url-2 = {http://dx.doi.org/10.1126/science.1103190}}
@article{PhysRevLett.110.130403,
Author = {Kumar, R. and Barrios, E. and Kupchak, C. and Lvovsky, A. I.},
Date-Added = {2016-08-01 16:40:14 +0000},
Date-Modified = {2016-08-01 16:40:14 +0000},
Doi = {10.1103/PhysRevLett.110.130403},
Issue = {13},
Journal = {Phys. Rev. Lett.},
Month = {Mar},
Numpages = {5},
Pages = {130403},
Publisher = {American Physical Society},
Title = {Experimental Characterization of Bosonic Creation and Annihilation Operators},
Url = {http://link.aps.org/doi/10.1103/PhysRevLett.110.130403},
Volume = {110},
Year = {2013},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.110.130403},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.110.130403}}
@article{PhysRevA.87.052320,
Author = {da Silva, Marcus P. and Guha, Saikat and Dutton, Zachary},
Date-Added = {2016-08-01 16:39:00 +0000},
Date-Modified = {2016-08-01 16:39:00 +0000},
Doi = {10.1103/PhysRevA.87.052320},
Issue = {5},
Journal = {Phys. Rev. A},
Month = {May},
Numpages = {7},
Pages = {052320},
Publisher = {American Physical Society},
Title = {Achieving minimum-error discrimination of an arbitrary set of laser-light pulses},
Url = {http://link.aps.org/doi/10.1103/PhysRevA.87.052320},
Volume = {87},
Year = {2013},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevA.87.052320},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevA.87.052320}}
@article{PhysRevLett.115.160505,
Author = {Poto\v{c}ek, V\'aclav and Miatto, Filippo M. and Mirhosseini, Mohammad and Maga\~na-Loaiza, Omar S. and Liapis, Andreas C. and Oi, Daniel K. L. and Boyd, Robert W. and Jeffers, John},
Date-Added = {2016-08-01 16:35:11 +0000},
Date-Modified = {2016-08-01 16:35:39 +0000},
Doi = {10.1103/PhysRevLett.115.160505},
Issue = {16},
Journal = {Phys. Rev. Lett.},
Month = {Oct},
Numpages = {5},
Pages = {160505},
Publisher = {American Physical Society},
Title = {Quantum Hilbert Hotel},
Url = {http://link.aps.org/doi/10.1103/PhysRevLett.115.160505},
Volume = {115},
Year = {2015},
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@article{PhysRevLett.110.210504,
Author = {Oi, Daniel K. L. and Poto\v{c}ek, V\'aclav and Jeffers, John},
Date-Added = {2016-08-01 16:32:49 +0000},
Date-Modified = {2016-08-01 16:33:43 +0000},
Doi = {10.1103/PhysRevLett.110.210504},
Issue = {21},
Journal = {Phys. Rev. Lett.},
Month = {May},
Numpages = {5},
Pages = {210504},
Publisher = {American Physical Society},
Title = {Nondemolition Measurement of the Vacuum State or its Complement},
Url = {http://link.aps.org/doi/10.1103/PhysRevLett.110.210504},
Volume = {110},
Year = {2013},
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@inbook{Lloyd2003,
Address = {Dordrecht},
Author = {Lloyd, Seth},
Booktitle = {Quantum Information with Continuous Variables},
Date-Added = {2016-08-01 16:26:16 +0000},
Date-Modified = {2016-08-01 16:27:55 +0000},
Doi = {10.1007/978-94-015-1258-9_5},
Editor = {Braunstein, Samuel L. and Pati, Arun K.},
Eprint = {arXiv:quant-ph/0008057},
Isbn = {978-94-015-1258-9},
Pages = {37--45},
Publisher = {Springer Netherlands},
Title = {Hybrid Quantum Computing},
Url = {http://dx.doi.org/10.1007/978-94-015-1258-9_5},
Year = {2003},
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@inproceedings{Gogioso2016Infinite-dimens,
Author = {Stefano Gogioso and Fabrizio Genovese},
Booktitle = {Proceedings of QPL 2016},
Citation_Arxiv_Id = {1605.04305},
Citation_Author = {Genovese, Fabrizio},
Citation_Date = {2016/05/12},
Citation_Online_Date = {2016/05/12},
Citation_Pdf_Url = {http://arxiv.org/pdf/1605.04305},
Citation_Title = {Infinite-dimensional Categorical Quantum Mechanics},
Date-Added = {2016-08-01 16:19:11 +0000},
Date-Modified = {2016-08-01 16:19:11 +0000},
Eprint = {arXiv:1605.04305},
Series = {EPTCS},
Title = {Infinite-dimensional Categorical Quantum Mechanics},
Year = {2016},
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@inproceedings{Zeng2014Abstract-struct,
Abstract = {We show that a pair of complementary dagger-Frobenius algebras, equipped with a self-conjugate comonoid homomorphism onto one of the algebras, produce a nontrivial unitary morphism on the product of the algebras. This gives an abstract understanding of the structure of an oracle in a quantum computation, and we apply this understanding to develop a new algorithm for the deterministic identification of group homomorphisms into abelian groups. We also discuss an application to the categorical theory of signal-flow networks.},
Author = {William Zeng and Jamie Vicary},
Booktitle = {Proceedings QPL 2014},
Citation_Arxiv_Id = {1406.1278},
Citation_Author = {Vicary, Jamie},
Citation_Date = {2014/06/05},
Citation_Doi = {10.4204/EPTCS.172.19},
Citation_Online_Date = {2014/12/30},
Citation_Pdf_Url = {http://arxiv.org/pdf/1406.1278},
Citation_Title = {Abstract structure of unitary oracles for quantum algorithms},
Date-Added = {2016-08-01 16:16:50 +0000},
Date-Modified = {2016-08-01 16:16:50 +0000},
Doi = {10.4204/EPTCS.172.19},
Eprint = {arXiv:1406.1278},
Pages = {270-284},
Series = {EPTCS},
Title = {Abstract structure of unitary oracles for quantum algorithms},
Volume = {172},
Year = {2014},
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@article{Comfort1977Ultrafilters:-S,
Author = {W. W. Comfort},
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Citation_Author = {Comfort, W. W.},
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Citation_Firstpage = {417},
Citation_Issn = {1936-881X},
Citation_Issue = {4},
Citation_Journal_Abbrev = {Bull. Amer. Math. Soc.},
Citation_Journal_Title = {Bulletin of the American Mathematical Society},
Citation_Lastpage = {455},
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Citation_Publication_Date = {1977},
Citation_Reference = {citation_author=Wallace, A. D.; citation_title=The structure of topological semigroups; citation_journal_title=Bull. Amer. Math. Soc.; citation_issn=0002-9904; citation_publication_date=1955; citation_volume=61; citation_firstpage=95; citation_lastpage=112},
Citation_Title = {Ultrafilters: Some old and some new results},
Citation_Volume = {83},
Date-Added = {2016-07-29 10:39:07 +0000},
Date-Modified = {2016-07-29 10:39:07 +0000},
Doi = {10.1090/S0002-9904-1977-14316-4},
Icbm = {41.836808, -71.412672},
Journal = {Bull. Amer. Math. Soc.},
Pages = {417-455},
Title = {Ultrafilters: Some old and some new results},
Volume = {83},
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@inproceedings{Duncan2016Interacting-Fro,
Author = {Ross Duncan and Kevin Dunne},
Booktitle = {{Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, {LICS} '16, New York, NY, USA, July 5-8, 2016}},
Date-Added = {2016-07-27 17:30:16 +0000},
Date-Modified = {2016-12-23 18:09:45 +0000},
Doi = {10.1145/2933575.2934550},
Editor = {Martin Grohe and Eric Koskinen and Natarajan Shankar},
Eprint = {arXiv:1601.04964},
Pages = {535--544},
Publisher = {{ACM}},
Series = {{LICS '16}},
Title = {Interacting {F}robenius Algebras are {H}opf},
Year = {2016},
Bdsk-Url-1 = {http://dx.doi.org/10.1145/2933575.2934550}}
@inproceedings{Andris-Ambainis2015Automata-and-Qu,
Abstract = {Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted models such as quantum versions of finite automata have been studied. In this paper, we survey various models of quantum finite automata and their properties. We also provide some open questions and new directions for researchers.},
Author = {Andris Ambainis and Abuzer Yakaryilmaz},
Booktitle = {Automata: From Mathematics to Applications},
Citation_Arxiv_Id = {1507.01988},
Citation_Author = {Yakaryilmaz, Abuzer},
Citation_Date = {2015/07/07},
Citation_Online_Date = {2015/07/07},
Citation_Pdf_Url = {http://arxiv.org/pdf/1507.01988},
Citation_Title = {Automata and Quantum Computing},
Date-Added = {2016-07-21 13:13:27 +0000},
Date-Modified = {2016-07-21 13:13:27 +0000},
Editor = {Jean-\'Eric Pin},
Eprint = {arXiv:1507.01988},
Title = {Automata and Quantum Computing},
Viewport = {width=device-width, initial-scale=1},
Year = {2015},
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@phdthesis{Mansfield2013The-Mathematica,
Author = {Shane Mansfield},
Date-Added = {2016-07-21 11:22:21 +0000},
Date-Modified = {2016-07-21 11:22:29 +0000},
School = {Oxford University},
Title = {The Mathematical Structure of Non-locality and Contextuality},
Year = {2013},
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@phdthesis{Backens2015Completeness-an,
Abstract = {Graphical languages offer intuitive and rigorous formalisms for quantum physics. They can be used to simplify expressions, derive equalities, and do computations. Yet in order to replace conventional formalisms, rigour alone is not sufficient: the new formalisms also need to have equivalent deductive power. This requirement is captured by the property of completeness, which means that any equality that can be derived using some standard formalism can also be derived graphically. In this thesis, I consider the ZX-calculus, a graphical language for pure state qubit quantum mechanics. I show that it is complete for pure state stabilizer quantum mechanics, so any problem within this fragment of quantum theory can be fully analysed using graphical methods. This includes questions of central importance in areas such as error-correcting codes or measurement-based quantum computation. Furthermore, I show that the ZX-calculus is complete for the single-qubit Clifford+T group, which is approximately universal: any single-qubit unitary can be approximated to arbitrary accuracy using only Clifford gates and the T-gate. [...] Lastly, I extend the use of rigorous graphical languages outside quantum theory to Spekkens' toy theory, a local hidden variable model that nevertheless exhibits some features commonly associated with quantum mechanics. [...] I develop a graphical calculus similar to the ZX-calculus that fully describes Spekkens' toy theory, and show that it is complete. Hence, stabilizer quantum mechanics and Spekkens' toy theory can be fully analysed and compared using graphical formalisms. Intuitive graphical languages can replace conventional formalisms for the analysis of many questions in quantum computation and foundations without loss of mathematical rigour or deductive power.},
Author = {Miriam Backens},
Citation_Arxiv_Id = {1602.08954},
Citation_Author = {Backens, Miriam},
Citation_Date = {2016/02/29},
Citation_Online_Date = {2016/02/29},
Citation_Pdf_Url = {http://arxiv.org/pdf/1602.08954},
Citation_Title = {Completeness and the ZX-calculus},
Date-Added = {2016-07-21 11:20:53 +0000},
Date-Modified = {2016-07-21 11:21:06 +0000},
Eprint = {arXiv:1602.08954},
School = {Oxford University},
Title = {Completeness and the ZX-calculus},
Viewport = {width=device-width, initial-scale=1},
Year = {2015},
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@phdthesis{Zeng2015The-Abstract-St,
Abstract = {Quantum information brings together theories of physics and computer science. This synthesis challenges the basic intuitions of both fields. In this thesis, we show that adopting a unified and general language for process theories advances foundations and practical applications of quantum information. Our first set of results analyze quantum algorithms with a process theoretic structure. We contribute new constructions of the Fourier transform and Pontryagin duality in dagger symmetric monoidal categories. We then use this setting to study generalized unitary oracles and give a new quantum blackbox algorithm for the identification of group homomorphisms, solving the GROUPHOMID problem. In the remaining section, we construct a novel model of quantum blackbox algorithms in non-deterministic classical computation. Our second set of results concerns quantum foundations. We complete work begun by Coecke et al., definitively connecting the Mermin non-locality of a process theory with a simple algebraic condition on that theory's phase groups. This result allows us to offer new experimental tests for Mermin non-locality and new protocols for quantum secret sharing. In our final chapter, we exploit the shared process theoretic structure of quantum information and distributional compositional linguistics. We propose a quantum algorithm adapted from Weibe et al. to classify sentences by meaning. The clarity of the process theoretic setting allows us to recover a speedup that is lost in the naive application of the algorithm. The main mathematical tools used in this thesis are group theory (esp. Fourier theory on finite groups), monoidal category theory, and categorical algebra.},
Author = {William Zeng},
Citation_Arxiv_Id = {1512.08062},
Citation_Author = {Zeng, William},
Citation_Date = {2015/12/26},
Citation_Online_Date = {2015/12/26},
Citation_Pdf_Url = {http://arxiv.org/pdf/1512.08062},
Citation_Title = {The Abstract Structure of Quantum Algorithms},
Date-Added = {2016-07-21 11:09:14 +0000},
Date-Modified = {2016-07-21 11:09:14 +0000},
Eprint = {arXiv:1512.08062},
School = {Oxford University},
Title = {The Abstract Structure of Quantum Algorithms},
Viewport = {width=device-width, initial-scale=1},
Year = {2015},
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@phdthesis{Quick2015-Logic,
Author = {David Quick},
Date-Added = {2016-07-21 11:06:56 +0000},
Date-Modified = {2016-07-21 11:07:03 +0000},
School = {Oxford University},
Title = {!-Logic},
Year = {2015},
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@phdthesis{Akhvlediani2011Relating-Types-,
Author = {Andrei Akhvlediani},
Date-Added = {2016-07-21 11:05:40 +0000},
Date-Modified = {2016-07-21 11:05:46 +0000},
School = {Oxford University},
Title = {Relating Types in Categorical Universal Algebra},
Year = {2011},
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@book{Vakil2015The-Rising-Sea:,
Author = {Ravi Vakil},
Date-Added = {2016-05-21 13:25:34 +0000},
Date-Modified = {2016-05-21 13:27:17 +0000},
Eprint = {math216.wordpress.com},
Keywords = {algebraic geometry; schemes; varieties},
Publisher = {draft},
Title = {The Rising Sea: Foundations of Algebraic Geometry},
Year = {2015},
Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGJCVYJHZlcnNpb25YJG9iamVjdHNZJGFyY2hpdmVyVCR0b3ASAAGGoKgHCBMUFRYaIVUkbnVsbNMJCgsMDxJXTlMua2V5c1pOUy5vYmplY3RzViRjbGFzc6INDoACgAOiEBGABIAFgAdccmVsYXRpdmVQYXRoWWFsaWFzRGF0YV8Qai4uLy4uLy4uLy4uLy4uL0RvY3VtZW50cy9SZWFkaW5nL1NjaWVuY2UvcGFwZXJzL1Zha2lsL1RoZSBSaXNpbmcgU2VhIEZvdW5kYXRpb25zIG9mIEFsZ2VicmFpYyBHZW9tZXRyeS5wZGbSFwsYGVdOUy5kYXRhTxECUAAAAAACUAACAAAMTWFjaW50b3NoIEhEAAAAAAAAAAAAAAAAAAAAzpiHAkgrAAABXGWKH1RoZSBSaXNpbmcgU2VhIEZvdW4jMTVDNTY5RC5wZGYAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAFcVp3SrLFhAAAAAAAAAAAABQAGAAAJIAAAAAAAAAAAAAAAAAAAAAVWYWtpbAAAEAAIAADOmHjyAAAAEQAIAADSrKNRAAAAAQAcAVxligAnAxkAJwMYACcDFwAKjkUACo5EAAJkfAACAGlNYWNpbnRvc2ggSEQ6VXNlcnM6AGt3YjEzMjE1OgBEb2N1bWVudHM6AFJlYWRpbmc6AFNjaWVuY2U6AHBhcGVyczoAVmFraWw6AFRoZSBSaXNpbmcgU2VhIEZvdW4jMTVDNTY5RC5wZGYAAA4AagA0AFQAaABlACAAUgBpAHMAaQBuAGcAIABTAGUAYQAgAEYAbwB1AG4AZABhAHQAaQBvAG4AcwAgAG8AZgAgAEEAbABnAGUAYgByAGEAaQBjACAARwBlAG8AbQBlAHQAcgB5AC4AcABkAGYADwAaAAwATQBhAGMAaQBuAHQAbwBzAGgAIABIAEQAEgBqVXNlcnMva3diMTMyMTUvRG9jdW1lbnRzL1JlYWRpbmcvU2NpZW5jZS9wYXBlcnMvVmFraWwvVGhlIFJpc2luZyBTZWEgRm91bmRhdGlvbnMgb2YgQWxnZWJyYWljIEdlb21ldHJ5LnBkZgATAAEvAAAVAAIAD///AACABtIbHB0eWiRjbGFzc25hbWVYJGNsYXNzZXNdTlNNdXRhYmxlRGF0YaMdHyBWTlNEYXRhWE5TT2JqZWN00hscIiNcTlNEaWN0aW9uYXJ5oiIgXxAPTlNLZXllZEFyY2hpdmVy0SYnVHJvb3SAAQAIABEAGgAjAC0AMgA3AEAARgBNAFUAYABnAGoAbABuAHEAcwB1AHcAhACOAPsBAAEIA1wDXgNjA24DdwOFA4kDkAOZA54DqwOuA8ADwwPIAAAAAAAAAgEAAAAAAAAAKAAAAAAAAAAAAAAAAAAAA8o=}}
@inproceedings{Reynolds02separationlogic:,
Author = {John C. Reynolds},
Booktitle = {In 17th LICS},
Date-Added = {2016-03-14 11:03:23 +0000},
Date-Modified = {2016-03-14 11:03:23 +0000},
Pages = {55--74},
Title = {Separation logic: A logic for shared mutable data structures},
Year = {2002},
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@misc{Eades-NSF-grant,
Author = {Harley Eades III},
Date-Added = {2016-03-14 10:53:54 +0000},
Date-Modified = {2016-03-14 10:55:25 +0000},
Howpublished = {NSF Standard Grant 1565557},
Title = {CRII: SHF: A New Foundation for Attack Trees Based on Monoidal Categories},
Year = {2016}}
@inbook{Wickerson2013Ribbon-Proofs-f,
Address = {Berlin, Heidelberg},
Author = {Wickerson, John and Dodds, Mike and Parkinson, Matthew},
Booktitle = {Programming Languages and Systems: 22nd European Symposium on Programming, ESOP 2013, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2013, Rome, Italy, March 16-24, 2013. Proceedings},
Date-Added = {2016-03-14 10:52:51 +0000},
Date-Modified = {2016-03-14 10:53:07 +0000},
Doi = {10.1007/978-3-642-37036-6{\_}12},
Editor = {Felleisen, Matthias and Gardner, Philippa},
Isbn = {978-3-642-37036-6},
Pages = {189--208},
Publisher = {Springer Berlin Heidelberg},
Title = {Ribbon Proofs for Separation Logic},
Ty = {CHAP},
Year = {2013},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-37036-6_12},
Bdsk-Url-2 = {http://dx.doi.org/10.1007/978-3-642-37036-6%7B%5C_%7D12}}
@inproceedings{Kissinger2015Quantomatic:-A-,
Author = {Kissinger, Aleks and Zamdzhiev, Vladimir},
Booktitle = {Automated Deduction - CADE-25: 25th International Conference on Automated Deduction, Berlin, Germany, August 1-7, 2015, Proceedings},
Date-Added = {2016-03-11 17:01:56 +0000},
Date-Modified = {2016-03-11 17:03:31 +0000},
Doi = {10.1007/978-3-319-21401-6_22},
Editor = {Felty, P. Amy and Middeldorp, Aart},
Eprint = {arXiv:1503.01034},
Isbn = {978-3-319-21401-6},
Pages = {326--336},
Publisher = {Springer},
Title = {Quantomatic: A Proof Assistant for Diagrammatic Reasoning},
Year = {2015},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-319-21401-6_22},
Bdsk-Url-2 = {http://dx.doi.org/10.1007/978-3-319-21401-6%7B%5C_%7D22}}
@article{OHalloran2012Automated-verif,
Abstract = {The CLawZ toolset independently and automatically proves the correctness of code automatically generated by a commercial auto-code generator for the Simulink modelling language. The use of formal methods is invisible to the user and it has been shown to lead to faster development of correct code. The CLawZ toolset has been continually developed and used for over a decade to prove the correctness of embedded real time safety critical software for Eurofighter Typhoon. The only requirement on the commercial auto-coder is that it provides traceability information between the signal wires in a Simulink{\textregistered} model and the program variables that implement them.},
Author = {O'Halloran, Colin},
Date-Added = {2016-03-11 09:40:10 +0000},
Date-Modified = {2016-03-11 09:40:10 +0000},
Doi = {10.1007/s10515-012-0116-5},
Journal = {Automated Software Engineering},
Number = {2},
Pages = {237--264},
Title = {Automated verification of code automatically generated from Simulink},
Volume = {20},
Year = {2012},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10515-012-0116-5}}
@article{Leroy-Compcert-CACM,
Abstract = {This paper reports on the development and formal verification (proof
of semantic preservation) of CompCert, a compiler from Clight (a
large subset of the C programming language) to PowerPC assembly code,
using the Coq proof assistant both for programming the compiler and
for proving its correctness. Such a verified compiler is useful in
the context of critical software and its formal verification: the
verification of the compiler guarantees that the safety properties
proved on the source code hold for the executable compiled code as
well.},
Author = {Xavier Leroy},
Date-Added = {2016-03-11 09:24:31 +0000},
Date-Modified = {2016-03-11 09:24:31 +0000},
Hal = {http://hal.archives-ouvertes.fr/inria-00415861/},
Journal = {Communications of the ACM},
Number = 7,
Pages = {107--115},
Pubkind = {journal-int-mono},
Title = {Formal verification of a realistic compiler},
Url = {http://gallium.inria.fr/~xleroy/publi/compcert-CACM.pdf},
Urlpublisher = {http://doi.acm.org/10.1145/1538788.1538814},
Volume = 52,
Year = 2009,
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@inproceedings{Denney2012AdvoCATE:-An-As,
Author = {Ewen Denney and Ganesh Pai and Joe Pohl},
Booktitle = {Proceedings of the Workshop on Next Generation of System Assurance Approaches for Safety Critical Systems (SASSUR)},
Date-Added = {2016-03-09 11:44:58 +0000},
Date-Modified = {2016-03-09 11:45:13 +0000},
Title = {AdvoCATE: An Assurance Case Automation Toolset},
Year = {2012},
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@article{JenLeif2015NoReturn,
Abstract = { At a fundamental level, the classical picture of the world is dead, and has been dead now for almost a century. Pinning down exactly which quantum phenomena are responsible for this has proved to be a tricky and controversial question, but a lot of progress has been made in the past few decades. We now have a range of precise statements showing that whatever the ultimate laws of nature are, they cannot be classical. In this article, we review results on the fundamental phenomena of quantum theory that cannot be understood in classical terms. We proceed by first granting quite a broad notion of classicality, describe a range of quantum phenomena (such as randomness, discreteness, the indistinguishability of states, measurement-uncertainty, measurement-disturbance, complementarity, non-commutativity, interference, the no-cloning theorem and the collapse of the wave-packet) that do fall under its liberal scope, and then finally describe some aspects of quantum physics that can never admit a classical understanding -- the intrinsically quantum mechanical aspects of nature. The most famous of these is Bell's theorem, but we also review two more recent results in this area. Firstly, Hardy's theorem shows that even a finite-dimensional quantum system must contain an infinite amount of information, and secondly, the Pusey--Barrett--Rudolph theorem shows that the wave function must be an objective property of an individual quantum system. Besides being of foundational interest, results of this sort now find surprising practical applications in areas such as quantum information science and the simulation of quantum systems. },
Author = {David Jennings and Matthew Leifer},
Date-Added = {2016-02-09 17:26:41 +0000},
Date-Modified = {2016-02-09 17:29:19 +0000},
Doi = {10.1080/00107514.2015.1063233},
Eprint = {arXiv:1501.03202},
Journal = {Contemporary Physics},
Pages = {1-23},
Title = {No return to classical reality},
Year = {2015},
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Bdsk-Url-1 = {http://dx.doi.org/10.1080/00107514.2015.1063233}}
@book{Sweedler1969Hopf-Algebras,
Author = {Moss E. Sweedler},
Date-Added = {2016-01-10 15:32:16 +0000},
Date-Modified = {2016-01-10 15:33:21 +0000},
Publisher = {W. A. Benjamin Inc.},
Title = {Hopf Algebras},
Year = {1969}}
@book{Harder2011Book,
Author = {G{\"u}nter Harder},
Date-Added = {2016-01-02 11:15:59 +0000},
Date-Modified = {2016-01-02 11:16:34 +0000},
Doi = {10.1007/978-3-8348-8330-8},
Publisher = {Springer},
Series = {Aspects of Mathematics},
Title = {Lectures on Algebraic Geometry I},
Volume = {35},
Year = {2011},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-8348-8330-8_4},
Bdsk-Url-2 = {http://dx.doi.org/10.1007/978-3-8348-8330-8}}
@incollection{Harder2011Cohomology-of-S,
Author = {G{\"u}nter Harder},
Booktitle = {Lectures on Algebraic Geometry I},
Date-Added = {2016-01-02 11:15:27 +0000},
Date-Modified = {2016-01-02 11:15:27 +0000},
Doi = {10.1007/978-3-8348-8330-8_4},
Pages = {51-178},
Publisher = {Springer},
Series = {Aspects of Mathematics},
Title = {Cohomology of Sheaves},
Volume = {35},
Year = {2011},
Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-8348-8330-8_4}}
@book{Sepanski2007Compact-Lie-Gro,
Author = {Mark R. Sepanski},
Date-Added = {2015-12-30 14:10:17 +0000},
Date-Modified = {2015-12-30 14:10:26 +0000},
Publisher = {Springer},
Series = {Graduate Texts in Mathematics},
Title = {Compact Lie Groups},
Volume = {235},
Year = {2007},
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@book{Geoghegan2008Topological-Met,
Author = {Ross Geoghegan},
Date-Added = {2015-12-30 14:07:43 +0000},
Date-Modified = {2015-12-30 14:07:43 +0000},
Series = {Graduate Texts in Mathematics},
Title = {Topological Methods in Group Theory},
Volume = {243},
Year = {2008},
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@book{Roman2008Advanced-Linear,
Author = {Steven Roman},
Date-Added = {2015-12-30 14:05:55 +0000},
Date-Modified = {2015-12-30 14:06:02 +0000},
Publisher = {Springer},
Series = {Graduate Texts in Mathematics},
Title = {Advanced Linear Algebra},
Volume = {135},
Year = {2008}}
@book{Christian-Kassel2008Braid-Groups,
Author = {Christian Kassel and Vladimir Turaev},
Date-Added = {2015-12-30 14:04:48 +0000},
Date-Modified = {2015-12-30 14:05:01 +0000},
Publisher = {Springer},
Series = {Graduate Texts in Mathematics},
Title = {Braid Groups},
Volume = {247},
Year = {2008},
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@book{Roe-Goodman2009Symmetry-Repres,
Author = {Roe Goodman and Nolan R. Wallach},
Date-Added = {2015-12-30 14:02:38 +0000},
Date-Modified = {2015-12-30 14:03:45 +0000},
Publisher = {Springer},
Series = {Graduate Texts in Mathematics},
Title = {Symmetry, Representations, and Invariants},
Volume = {255},
Year = {2009},
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@book{Wilson2009The-Finite-Simp,
Author = {Robert A. Wilson},
Date-Added = {2015-12-30 14:00:05 +0000},
Date-Modified = {2015-12-30 14:00:46 +0000},
Publisher = {Springer},
Series = {Graduate Texts in Mathematics},
Title = {The Finite Simple Groups},
Volume = {251},
Year = {2009},
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@book{Serre2010Matrices-Theory,
Author = {Denis Serre},
Date-Added = {2015-12-30 13:57:46 +0000},
Date-Modified = {2015-12-30 13:59:09 +0000},
Publisher = {Springer},
Series = {Graduate Texts in Mathematics},
Title = {Matrices Theory and Applications},
Volume = {216},
Year = {2010},
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@book{Lee2011Introduction-to,
Author = {John M. Lee},
Date-Added = {2015-12-30 13:55:57 +0000},
Date-Modified = {2015-12-30 13:56:20 +0000},
Publisher = {Springer},
Series = {Graduate Texts in Mathematics},
Title = {Introduction to Topological Manifolds},
Volume = {202},
Year = {2011},
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@book{Kemper2011A-Course-in-Com,
Author = {Gregor Kemper},
Date-Added = {2015-12-30 13:54:32 +0000},
Date-Modified = {2015-12-30 13:55:15 +0000},
Publisher = {Springer},
Series = {Graduate Texts in Mathematics},
Title = {A Course in Commutative Algebra},
Volume = {256},
Year = {2011},
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@book{Schmudgen2012Unbounded-Self-,
Author = {Konrad Schm\"udgen},
Date-Added = {2015-12-30 13:52:54 +0000},
Date-Modified = {2015-12-30 13:53:45 +0000},
Publisher = {Springer},
Series = {Graduate Texts in Mathematics},
Title = {Unbounded Self-adjoint Operators on Hilbert Space},
Volume = {265},
Year = {2012},
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@book{Zhu2012Analysis-on-Foc,
Author = {Kehe Zhu},
Date-Added = {2015-12-30 13:51:34 +0000},
Date-Modified = {2015-12-30 13:51:58 +0000},
Publisher = {Springer},
Series = {Graduate Texts in Mathematics},
Title = {Analysis on Fock Spaces},
Volume = {263},
Year = {2012},
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@book{Lee2012Introduction-to,
Author = {John M. Lee},
Date-Added = {2015-12-30 13:50:30 +0000},
Date-Modified = {2015-12-30 13:50:45 +0000},
Publisher = {Springer},
Series = {Graduate Texts in Mathematics},
Title = {Introduction to Smooth Manifolds},
Volume = {218},
Year = {2012},
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@book{Bump2013Lie-Groups,
Author = {Daniel Bump},
Date-Added = {2015-12-30 13:48:31 +0000},
Date-Modified = {2015-12-30 13:48:51 +0000},
Doi = {10.1007/978-1-4614-8024-2},
Publisher = {Springer},
Series = {Graduate Texts in Mathematics},
Title = {Lie Groups},
Volume = {225},
Year = {2013},
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@book{Hall2013Quantum-Theory-,
Author = {Brian C. Hall},
Date-Added = {2015-12-30 13:46:55 +0000},
Date-Modified = {2015-12-30 13:47:48 +0000},
Doi = {10.1007/978-1-4614-7116-5},
Publisher = {Springer},
Series = {Graduate Texts in Mathematics},
Title = {Quantum Theory for Mathematicians},
Volume = {267},
Year = {2013},
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@book{Weintraub2014Fundamentals-of,
Author = {Steven H. Weintraub},
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Doi = {10.1007/978-1-4939-1844-7},
Publisher = {Springer},
Series = {Graduate Texts in Mathematics},
Title = {Fundamentals of Algebraic Topology},
Volume = {270},
Year = {2014},
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@book{Osborne2014Locally-Convex-,
Author = {M. Scott Osborne},
Date-Added = {2015-12-30 13:41:50 +0000},
Date-Modified = {2015-12-30 13:42:27 +0000},
Doi = {10.1007/978-3-319-02045-7},
Publisher = {Springer},
Series = {Graduate Texts in Mathematics},
Title = {Locally Convex Spaces},
Volume = {269},
Year = {2014},
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@book{Hall2015Lie-Groups-Lie-,
Author = {Brian C. Hall},
Date-Added = {2015-12-30 13:39:20 +0000},
Date-Modified = {2015-12-30 13:40:21 +0000},
Doi = {10.1007/978-3-319-13467-3},
Publisher = {Springer},
Series = {Graduate Texts in Mathematics},
Title = {Lie Groups, Lie Algebras, and Representations An Elementary Introduction},
Volume = {222},
Year = {2015},
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@inproceedings{KellyCoherenceLaxAlgsDistLaws1974,
Author = {G. M. Kelly},
Booktitle = {Proceedings Sydney Category Theory Seminar 1972/1973},
Date-Added = {2015-12-30 13:24:18 +0000},
Date-Modified = {2015-12-30 13:25:31 +0000},
Doi = {10.1007/BFb0063096},
Editor = {Gregory M. Kelly},
Publisher = {Springer},
Series = {Lecture Notes in Mathematics},
Title = {Coherence theorems for lax algebras and for distributive laws},
Volume = {420},
Year = {1974},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/BFb0063096}}
@inproceedings{KellyDoctrinalAdjunction1974,
Author = {G. M. Kelly},
Booktitle = {Proceedings Sydney Category Theory Seminar 1972/1973},
Date-Added = {2015-12-30 13:22:19 +0000},
Date-Modified = {2015-12-30 13:23:32 +0000},
Doi = {10.1007/BFb0063096},
Editor = {Gregory M. Kelly},
Pages = {275-280},
Publisher = {Springer},
Series = {Lecture Notes in Mathematics},
Title = {Doctrinal adjunction},
Volume = {420},
Year = {1974},
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@inproceedings{StreetCosmoi1974,
Author = {Ross Street},
Booktitle = {Proceedings Sydney Category Theory Seminar 1972/1973},
Date-Added = {2015-12-30 13:21:10 +0000},
Date-Modified = {2015-12-30 13:22:17 +0000},
Doi = {10.1007/BFb0063096},
Editor = {Gregory M. Kelly},
Pages = {143-180},
Publisher = {Springer},
Series = {Lecture Notes in Mathematics},
Title = {Elementary cosmoi I},
Volume = {420},
Year = {1974},
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@inproceedings{StreetFibreYoneda1974,
Author = {Ross Street},
Booktitle = {Proceedings Sydney Category Theory Seminar 1972/1973},
Date-Added = {2015-12-30 13:20:01 +0000},
Date-Modified = {2015-12-30 13:20:59 +0000},
Doi = {10.1007/BFb0063096},
Editor = {Gregory M. Kelly},
Pages = {104-133},
Publisher = {Springer},
Series = {Lecture Notes in Mathematics},
Title = {Fibrations and Yoneda's lemma in a 2-category},
Volume = {420},
Year = {1974},
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@inproceedings{KellyStreet2CatsReview1974,
Author = {G. M. Kelly and Ross Street},
Booktitle = {Proceedings Sydney Category Theory Seminar 1972/1973},
Date-Added = {2015-12-30 13:17:14 +0000},
Date-Modified = {2015-12-30 13:18:10 +0000},
Doi = {10.1007/BFb0063096},
Editor = {Gregory M. Kelly},
Pages = {75-103},
Publisher = {Springer},
Series = {Lecture Notes in Mathematics},
Title = {Review of the elements of 2-categories},
Volume = {420},
Year = {1974},
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@inproceedings{DayLimit1974,
Author = {Brian Day},
Booktitle = {Proceedings Sydney Category Theory Seminar 1972/1973},
Date-Added = {2015-12-30 13:15:29 +0000},
Date-Modified = {2015-12-30 13:15:57 +0000},
Doi = {10.1007/BFb0063096},
Editor = {Gregory M. Kelly},
Pages = {65-74},
Publisher = {Springer},
Series = {Lecture Notes in Mathematics},
Title = {Limit spaces and closed span categories},
Volume = {420},
Year = {1974},
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@inproceedings{DayEmbedding1974,
Author = {Brian Day},
Booktitle = {Proceedings Sydney Category Theory Seminar 1972/1973},
Date-Added = {2015-12-30 13:14:05 +0000},
Date-Modified = {2015-12-30 13:15:09 +0000},
Doi = {10.1007/BFb0063096},
Editor = {Gregory M. Kelly},
Pages = {55-64},
Publisher = {Springer},
Series = {Lecture Notes in Mathematics},
Title = {An embedding theorem for closed categories},
Volume = {420},
Year = {1974},
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@inproceedings{Dayclosedcats1974,
Author = {Brian Day},
Booktitle = {Proceedings Sydney Category Theory Seminar 1972/1973},
Date-Added = {2015-12-30 13:10:38 +0000},
Date-Modified = {2015-12-30 13:14:05 +0000},
Doi = {10.1007/BFb0063096},
Editor = {Gregory M. Kelly},
Pages = {20-54},
Publisher = {Springer},
Series = {Lecture Notes in Mathematics},
Title = {On closed categories of functors II},
Volume = {420},
Year = {1974},
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@inproceedings{Day1974On-adjoint-func,
Author = {Brian Day},
Booktitle = {Proceedings Sydney Category Theory Seminar 1972/1973},
Date-Added = {2015-12-30 13:10:18 +0000},
Date-Modified = {2015-12-30 13:10:18 +0000},
Doi = {10.1007/BFb0063096},
Editor = {Gregory M. Kelly},
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Pages = {1-19},
Publisher = {Springer},
Series = {Lecture Notes in Mathematics},
Title = {On adjoint-functor factorisation},
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@article{Lee201278,
Abstract = {This paper proposes a novel scheme for constructing reversible Turing machines (RTMs) via various reversible logic elements. A reversible logic element is similar to a conventional reversible logic gate, except that the element also carries a 1-bit memory that can store binary states. The usage of internal states allows much more efficient and straightforward constructions of \{RTMs\} based on reversible elements than based on reversible logic gates. In particular, a remarkable feature of our constructions is that they can operate asynchronously, whereby the clock signal, which is indispensable for synchronizing all elements as in a reversible logic circuit, can possibly be removed from the construction. },
Author = {Jia Lee and Rui-Long Yang and Kenichi Morita},
Date-Added = {2015-12-20 13:41:56 +0000},
Date-Modified = {2015-12-20 13:41:56 +0000},
Doi = {http://dx.doi.org/10.1016/j.tcs.2012.07.027},
Issn = {0304-3975},
Journal = {Theoretical Computer Science},
Keywords = {Asynchronous operation},
Pages = {78 - 88},
Title = {Design of 1-tape 2-symbol reversible Turing machines based on reversible logic elements},
Url = {http://www.sciencedirect.com/science/article/pii/S0304397512007359},
Volume = {460},
Year = {2012},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0304397512007359},
Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.tcs.2012.07.027}}
@article{Morita20113856,
Abstract = {In this paper, we investigate how 1-D reversible cellular automata (RCAs) can simulate reversible Turing machines (RTMs) and cyclic tag systems (CTSs). A \{CTS\} is a universal string rewriting system proposed by M. Cook. First, we show that for any m -state n -symbol \{RTM\} there is a 1-D 2-neighbor \{RCA\} with a number of states less than ( m + 2 n + 1 ) ( m + n + 1 ) that simulates it. It improves past results both in the number of states and in the neighborhood size. Second, we study the problem of finding a 1-D \{RCA\} with a small number of states that can simulate any CTS. So far, a 30-state \{RCA\} that can simulate any \{CTS\} and works on ultimately periodic infinite configurations has been given by K. Morita. Here, we show there is a 24-state 2-neighbor \{RCA\} with this property. },
Author = {Kenichi Morita},
Date-Added = {2015-12-20 12:57:54 +0000},
Date-Modified = {2015-12-20 12:57:54 +0000},
Doi = {http://dx.doi.org/10.1016/j.tcs.2011.02.022},
Issn = {0304-3975},
Journal = {Theoretical Computer Science},
Keywords = {Cyclic tag system},
Note = {Cellular Automata and Discrete Complex Systems},
Number = {30},
Pages = {3856 - 3865},
Title = {Simulating reversible Turing machines and cyclic tag systems by one-dimensional reversible cellular automata},
Url = {http://www.sciencedirect.com/science/article/pii/S0304397511001423},
Volume = {412},
Year = {2011},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0304397511001423},
Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.tcs.2011.02.022}}
@incollection{AxelsenGluckURTM2011,
Author = {Axelsen, HolgerBock and Gl{\"u}ck, Robert},
Booktitle = {Language and Automata Theory and Applications},
Date-Added = {2015-12-20 12:55:10 +0000},
Date-Modified = {2015-12-20 12:55:54 +0000},
Doi = {10.1007/978-3-642-21254-3_8},
Editor = {Dediu, Adrian-Horia and Inenaga, Shunsuke and Mart{\'\i}n-Vide, Carlos},
Isbn = {978-3-642-21253-6},
Language = {English},
Pages = {117-128},
Publisher = {Springer Berlin Heidelberg},
Series = {Lecture Notes in Computer Science},
Title = {A Simple and Efficient Universal Reversible Turing Machine},
Url = {http://dx.doi.org/10.1007/978-3-642-21254-3_8},
Volume = {6638},
Year = {2011},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-21254-3_8}}
@article{Morita2008101,
Abstract = {Reversible computing is a paradigm where computing models are defined so that they reflect physical reversibility, one of the fundamental microscopic physical property of Nature. In this survey/tutorial paper, we discuss how computation can be carried out in a reversible system, how a universal reversible computer can be constructed by reversible logic elements, and how such logic elements are related to reversible physical phenomena. We shall see that, in reversible systems, computation can often be carried out in a very different manner from conventional (i.e., irreversible) computing systems, and even very simple reversible systems or logic elements have computation- or logical-universality. We discuss these problems based on reversible logic elements/circuits, reversible Turing machines, reversible cellular automata, and some other related models of reversible computing. },
Author = {Kenichi Morita},
Date-Added = {2015-12-20 12:53:10 +0000},
Date-Modified = {2015-12-20 12:53:10 +0000},
Doi = {http://dx.doi.org/10.1016/j.tcs.2008.01.041},
Issn = {0304-3975},
Journal = {Theoretical Computer Science},
Keywords = {Computation-universality},
Number = {1},
Pages = {101 - 131},
Title = {Reversible computing and cellular automata---A survey},
Url = {http://www.sciencedirect.com/science/article/pii/S030439750800100X},
Volume = {395},
Year = {2008},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S030439750800100X},
Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.tcs.2008.01.041}}
@article{Gogioso2015Operational-Mer,
Abstract = {Contextuality is a key resource in quantum information and the device-independent security of quantum algorithms. In this work, we show that the recently developed, operational Mermin non-locality arguments provide a large, novel family of quantum realisable All-vs-Nothing models. In particular, they result in a diverse wealth of quantum realisable models which are maximally contextual (i.e. lie on the faces of the no-signalling polytope with no local elements), and could be used as a resource for the security of a new class of quantum secret sharing algorithms.},
Author = {Stefano Gogioso},
Citation_Arxiv_Id = {1510.03419},
Citation_Author = {Gogioso, Stefano},
Citation_Date = {2015/10/11},
Citation_Online_Date = {2015/10/11},
Citation_Pdf_Url = {http://arxiv.org/pdf/1510.03419},
Citation_Title = {Operational Mermin non-locality and All-vs-Nothing arguments},
Date-Added = {2015-12-07 15:08:58 +0000},
Date-Modified = {2015-12-07 15:08:58 +0000},
Eprint = {arXiv:1510.03419},
Journal = {arXiv.org},
Title = {Operational Mermin non-locality and All-vs-Nothing arguments},
Year = {2015},
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@article{Spivak2015The-steady-stat,
Abstract = {Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be arranged in series, in parallel, and with feedback to form a new dynamical system---this is called compositionality---and the process can be repeated in a fractal-like manner to form more complex systems of systems. One issue is that as larger systems are created, their state space grows exponentially. In this paper a technique for calculating the steady states of a system of systems, in terms of the steady states of its component dynamical systems, is provided. These are organized into "steady state matrices" which are strongly analogous to bifurcation diagrams. It is shown that the compositionality structure of dynamical systems fits with the familiar monoidal structure for the steady state matrices, where serial, parallel, and feedback composition of matrices correspond to multiplication, Kronecker product, and partial trace operations. The steady state matrices of dynamical systems respect this compositionality structure, exponentially reducing the complexity involved in studying the steady states of composite dynamical systems.},
Author = {David I. Spivak},
Citation_Arxiv_Id = {1512.00802},
Citation_Author = {Spivak, David I.},
Citation_Date = {2015/12/02},
Citation_Online_Date = {2015/12/02},
Citation_Pdf_Url = {http://arxiv.org/pdf/1512.00802},
Citation_Title = {The steady states of coupled dynamical systems compose according to matrix arithmetic},
Date-Added = {2015-12-07 15:07:31 +0000},
Date-Modified = {2015-12-07 15:07:31 +0000},
Eprint = {arXiv:1512.00802},
Journal = {arXiv.org},
Title = {The steady states of coupled dynamical systems compose according to matrix arithmetic},
Year = {2015},
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@article{Vagner2015Algebras-of-Ope,
Abstract = {In this paper, we use the language of operads to study open dynamical systems. More specifically, we study the algebraic nature of assembling complex dynamical systems from an interconnection of simpler ones. The syntactic architecture of such interconnections is encoded using the visual language of wiring diagrams. We define the symmetric monoidal category W, from which we may construct an operad O(W), whose objects are black boxes with input and output ports, and whose morphisms are wiring diagrams, thus prescribing the algebraic rules for interconnection. We then define two W-algebras, G and L, which associate semantic content to the structures in W. Respectively, they correspond to general and to linear systems of differential equations, in which an internal state is controlled by inputs and produces outputs. As an example, we use these algebras to formalize the classical problem of systems of tanks interconnected by pipes, and hence make explicit the algebraic relationships among systems at different levels of granularity.},
Author = {Dmitry Vagner and David I. Spivak and Eugene Lerman},
Citation_Arxiv_Id = {1408.1598},
Citation_Author = {Lerman, Eugene},
Citation_Date = {2014/08/07},
Citation_Online_Date = {2015/10/02},
Citation_Pdf_Url = {http://arxiv.org/pdf/1408.1598},
Citation_Title = {Algebras of Open Dynamical Systems on the Operad of Wiring Diagrams},
Date-Added = {2015-12-07 15:05:26 +0000},
Date-Modified = {2016-03-14 09:08:14 +0000},
Eprint = {arXiv:1408.1598},
Journal = {Theory and Applications of Categories},
Number = {51},
Pages = {1793-1822},
Title = {Algebras of Open Dynamical Systems on the Operad of Wiring Diagrams},
Volume = {30},
Year = {2015},
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@article{Spivak2013The-operad-of-w,
Abstract = {Wiring diagrams, as seen in digital circuits, can be nested hierarchically and thus have an aspect of self-similarity. We show that wiring diagrams form the morphisms of an operad $\mcT$\mcT, capturing this self-similarity. We discuss the algebra $\Rel$\Rel of mathematical relations on $\mcT$\mcT, and in so doing use wiring diagrams as a graphical language with which to structure queries on relational databases. We give the example of circuit diagrams as a special case. We move on to show how plug-and-play devices and also recursion can be formulated in the operadic framework as well. Throughout we include many examples and figures.},
Author = {David I. Spivak},
Citation_Arxiv_Id = {1305.0297},
Citation_Author = {Spivak, David I.},
Citation_Date = {2013/05/01},
Citation_Online_Date = {2013/05/01},
Citation_Pdf_Url = {http://arxiv.org/pdf/1305.0297},
Citation_Title = {The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits},
Date-Added = {2015-12-07 15:03:20 +0000},
Date-Modified = {2015-12-07 15:03:20 +0000},
Eprint = {arXiv:1305.0297},
Journal = {arXiv.org},
Title = {The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits},
Year = {2013},
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@article{Rupel2013The-operad-of-t,
Abstract = {We investigate the hierarchical structure of processes using the mathematical theory of operads. Information or material enters a given process as a stream of inputs, and the process converts it to a stream of outputs. Output streams can then be supplied to other processes in an organized manner, and the resulting system of interconnected processes can itself be considered a macro process. To model the inherent structure in this kind of system, we define an operad \mathcal{W} of black boxes and directed wiring diagrams, and we define a \mathcal{W}-algebra \mathcal{P} of processes (which we call propagators, after Radul and Sussman). Previous operadic models of wiring diagrams use undirected wires without length, useful for modeling static systems of constraints, whereas we use directed wires with length, useful for modeling dynamic flows of information. We give multiple examples throughout to ground the ideas.},
Author = {Dylan Rupel and David I. Spivak},
Citation_Arxiv_Id = {1307.6894},
Citation_Author = {Spivak, David I.},
Citation_Date = {2013/07/25},
Citation_Online_Date = {2013/07/25},
Citation_Pdf_Url = {http://arxiv.org/pdf/1307.6894},
Citation_Title = {The operad of temporal wiring diagrams: formalizing a graphical language for discrete-time processes},
Date-Added = {2015-12-07 15:01:35 +0000},
Date-Modified = {2015-12-07 15:01:35 +0000},
Eprint = {arXiv:1307.6894},
Journal = {arXiv.org},
Title = {The operad of temporal wiring diagrams: formalizing a graphical language for discrete-time processes},
Year = {2013},
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@incollection{Wiesner2009qca,
Author = {Wiesner, Karoline},
Booktitle = {Encyclopedia of Complexity and Systems Science},
Date-Added = {2015-12-07 14:51:09 +0000},
Date-Modified = {2015-12-07 14:51:19 +0000},
Doi = {10.1007/978-0-387-30440-3_426},
Editor = {Meyers, Robert A.},
Isbn = {978-0-387-75888-6},
Language = {English},
Pages = {7154-7164},
Publisher = {Springer New York},
Title = {Quantum Cellular Automata},
Url = {http://dx.doi.org/10.1007/978-0-387-30440-3_426},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-0-387-30440-3_426}}
@article{Kari20053,
Abstract = {This article surveys some theoretical aspects of cellular automata \{CA\} research. In particular, we discuss classical and new results on reversibility, conservation laws, limit sets, decidability questions, universality and topological dynamics of CA. The selection of topics is by no means comprehensive and reflects the research interests of the author. The main goal is to provide a tutorial of \{CA\} theory to researchers in other branches of natural computing, to give a compact collection of known results with references to their proofs, and to suggest some open problems. },
Author = {Jarkko Kari},
Date-Added = {2015-12-07 14:47:56 +0000},
Date-Modified = {2015-12-07 14:47:56 +0000},
Doi = {http://dx.doi.org/10.1016/j.tcs.2004.11.021},
Issn = {0304-3975},
Journal = {Theoretical Computer Science},
Keywords = {Discrete dynamical system},
Number = {1--3},
Pages = {3 - 33},
Title = {Theory of cellular automata: A survey},
Url = {http://www.sciencedirect.com/science/article/pii/S030439750500054X},
Volume = {334},
Year = {2005},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S030439750500054X},
Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.tcs.2004.11.021}}
@incollection{BPS-holomorphic-1994,
Author = {Blute, R.F. and Panangaden, Prakash and Seely, R.A.G.},
Booktitle = {Mathematical Foundations of Programming Semantics},
Date-Added = {2015-12-07 11:47:56 +0000},
Date-Modified = {2015-12-07 11:48:40 +0000},
Doi = {10.1007/3-540-58027-1_23},
Editor = {Brookes, Stephen and Main, Michael and Melton, Austin and Mislove, Michael and Schmidt, David},
Isbn = {978-3-540-58027-0},
Keywords = {Fock space; linear logic; Banach spaces; holomorphic functions; quantum field theory},
Language = {English},
Pages = {474-512},
Publisher = {Springer Berlin Heidelberg},
Series = {Lecture Notes in Computer Science},
Title = {Holomorphic models of exponential types in linear logic},
Url = {http://dx.doi.org/10.1007/3-540-58027-1_23},
Volume = {802},
Year = {1994},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/3-540-58027-1_23}}
@incollection{Stierer2008Learning-to-wri,
Author = {Stierer, Barry},
Booktitle = {The scholarship of teaching and learning in higher education},
Date-Added = {2015-11-25 01:13:34 +0000},
Date-Modified = {2015-11-25 01:13:34 +0000},
Pages = {34-45},
Publisher = {Society for Research into Higher Educaton & Open University Press},
Title = {Learning to write about teaching: understanding the writing demands of lecturer development programmes in higher education},
Year = {2008},
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@book{wenger1999communities,
Author = {Wenger, E.},
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Isbn = {9780521663632},
Lccn = {98202423},
Publisher = {Cambridge University Press},
Series = {Learning in Doing: Social, Cognitive and Computational Perspectives},
Title = {Communities of Practice: Learning, Meaning, and Identity},
Url = {https://books.google.co.uk/books?id=heBZpgYUKdAC},
Year = {1999},
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@article{Shulman2005Pedagogies-of-u,
Author = {Shulman, Lee S.},
Date-Added = {2015-11-25 00:58:24 +0000},
Date-Modified = {2015-11-25 00:58:24 +0000},
Journal = {Liberal Education},
Number = {2},
Pages = {18-25},
Title = {Pedagogies of uncertainty},
Volume = {91},
Year = {2005},
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@incollection{Middendorf2004Decoding-the-Di,
Author = {Joan Middendorf and David Pace},
Booktitle = {Decoding the Disciplines: Helping Students Learn Disciplinary Ways of Thinking},
Chapter = {1},
Date-Added = {2015-11-25 00:54:10 +0000},
Date-Modified = {2015-11-25 00:55:54 +0000},
Editor = {David Pace and Joan Middendorf},
Number = {98},
Publisher = {Wiley},
Series = {New Directions for Teaching and Learning},
Title = {Decoding the Disciplines: A Model for Helping Students Learn Disciplinary Ways of Thinking},
Year = {2004},
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@article{10.2307/20027998,
Author = {Lee S. Shulman},
Date-Added = {2015-11-25 00:51:05 +0000},
Date-Modified = {2015-11-25 00:51:05 +0000},
Issn = {00115266},
Journal = {Daedalus},
Number = {3},
Pages = {52-59},
Publisher = {The MIT Press},
Title = {Signature Pedagogies in the Professions},
Url = {http://www.jstor.org/stable/20027998},
Volume = {134},
Year = {2005},
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@article{PhysRevA.89.052126,
Author = {Kunjwal, Ravi and Heunen, Chris and Fritz, Tobias},
Date-Added = {2015-11-13 11:28:31 +0000},
Date-Modified = {2015-11-13 11:28:31 +0000},
Doi = {10.1103/PhysRevA.89.052126},
Issue = {5},
Journal = {Phys. Rev. A},
Month = {May},
Numpages = {5},
Pages = {052126},
Publisher = {American Physical Society},
Title = {Quantum realization of arbitrary joint measurability structures},
Url = {http://link.aps.org/doi/10.1103/PhysRevA.89.052126},
Volume = {89},
Year = {2014},
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@article{PhysRevA.89.032121,
Author = {Heunen, Chris and Fritz, Tobias and Reyes, Manuel L.},
Date-Added = {2015-11-13 11:26:40 +0000},
Date-Modified = {2015-11-13 11:26:40 +0000},
Doi = {10.1103/PhysRevA.89.032121},
Issue = {3},
Journal = {Phys. Rev. A},
Month = {Mar},
Numpages = {5},
Pages = {032121},
Publisher = {American Physical Society},
Title = {Quantum theory realizes all joint measurability graphs},
Url = {http://link.aps.org/doi/10.1103/PhysRevA.89.032121},
Volume = {89},
Year = {2014},
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@inproceedings{EPTCS171.6,
Author = {Fritz, Tobias and Leverrier, Anthony and Sainz, Ana Bel\'en},
Booktitle = {{\rm Proceedings of the 10th International Workshop on} Quantum Physics and Logic, {\rm Castelldefels (Barcelona), Spain, 17th to 19th July 2013}},
Date-Added = {2015-11-13 11:25:00 +0000},
Date-Modified = {2015-11-13 11:25:00 +0000},
Doi = {10.4204/EPTCS.171.6},
Editor = {Coecke, Bob and Hoban, Matty},
Pages = {63-70},
Publisher = {Open Publishing Association},
Series = {Electronic Proceedings in Theoretical Computer Science},
Title = {Probabilistic models on contextuality scenarios},
Volume = {171},
Year = {2014},
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Bdsk-Url-1 = {http://dx.doi.org/10.4204/EPTCS.171.6}}
@article{Acin2015combinatorial-nonlocality,
Author = {Ac{\'\i}n, Antonio and Fritz, Tobias and Leverrier, Anthony and Sainz, AnaBel{\'e}n},
Date-Added = {2015-11-13 11:22:16 +0000},
Date-Modified = {2015-11-13 11:22:44 +0000},
Doi = {10.1007/s00220-014-2260-1},
Issn = {0010-3616},
Journal = {Communications in Mathematical Physics},
Language = {English},
Number = {2},
Pages = {533-628},
Publisher = {Springer Berlin Heidelberg},
Title = {A Combinatorial Approach to Nonlocality and Contextuality},
Url = {http://dx.doi.org/10.1007/s00220-014-2260-1},
Volume = {334},
Year = {2015},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00220-014-2260-1}}
@article{Fritz2013Local-orthogona,
Author = {Fritz, T. and Sainz, A. B. and Augusiak, R. and Brask, J Bohr and Chaves, R. and Leverrier, A. and Acin, A.},
Date = {2013/08/16/online},
Date-Added = {2015-11-13 11:21:04 +0000},
Date-Modified = {2015-11-13 11:21:04 +0000},
Day = {16},
Journal = {Nat Commun},
L3 = {10.1038/ncomms3263},
M3 = {Article},
Month = {08},
Publisher = {Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
Title = {Local orthogonality as a multipartite principle for quantum correlations},
Ty = {JOUR},
Url = {http://dx.doi.org/10.1038/ncomms3263},
Volume = {4},
Year = {2013},
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Bdsk-Url-1 = {http://dx.doi.org/10.1038/ncomms3263}}
@article{Cabello2010Non-Contextuali,
Abstract = {We show that the noncontextual inequality proposed by Klyachko et al. [Phys. Rev. Lett. 101, 020403 (2008)] belongs to a broader family of inequalities, one associated to each compatibility structure of a set of events (a graph), and its independence number. These have the surprising property that the maximum quantum violation is given by the Lovasz theta-function of the graph, which was originally proposed as an upper bound on its Shannon capacity. Furthermore, probabilistic theories beyond quantum mechanics may have an even larger violation, which is given by the so-called fractional packing number. We discuss in detail, and compare, the sets of probability distributions attainable by noncontextual, quantum, and generalized models; the latter two are shown to have semidefinite and linear characterizations, respectively. The implications for Bell inequalities, which are examples of noncontextual inequalities, are discussed. In particular, we show that every Bell inequality can be recast as a noncontextual inequality a la Klyachko et al.},
Author = {Adan Cabello and Simone Severini and Andreas Winter},
Citation_Arxiv_Id = {1010.2163},
Citation_Author = {Winter, Andreas},
Citation_Date = {2010/10/11},
Citation_Online_Date = {2010/10/11},
Citation_Pdf_Url = {http://arxiv.org/pdf/1010.2163},
Citation_Title = {(Non-)Contextuality of Physical Theories as an Axiom},
Date-Added = {2015-11-13 11:13:19 +0000},
Date-Modified = {2015-11-13 11:13:19 +0000},
Eprint = {arXiv:1010.2163},
Journal = {ArXiv.org},
Title = {(Non-)Contextuality of Physical Theories as an Axiom},
Year = {2010},
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@article{PhysRevLett.112.040401,
Author = {Cabello, Ad\'an and Severini, Simone and Winter, Andreas},
Date-Added = {2015-11-13 11:06:50 +0000},
Date-Modified = {2015-11-13 11:06:50 +0000},
Doi = {10.1103/PhysRevLett.112.040401},
Issue = {4},
Journal = {Phys. Rev. Lett.},
Month = {Jan},
Numpages = {5},
Pages = {040401},
Publisher = {American Physical Society},
Title = {Graph-Theoretic Approach to Quantum Correlations},
Url = {http://link.aps.org/doi/10.1103/PhysRevLett.112.040401},
Volume = {112},
Year = {2014},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.112.040401},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.112.040401}}
@article{PhysRevLett.114.250402,
Author = {Cabello, Ad\'an and Kleinmann, Matthias and Budroni, Costantino},
Date-Added = {2015-11-13 11:05:02 +0000},
Date-Modified = {2015-11-13 11:05:02 +0000},
Doi = {10.1103/PhysRevLett.114.250402},
Issue = {25},
Journal = {Phys. Rev. Lett.},
Month = {Jun},
Numpages = {5},
Pages = {250402},
Publisher = {American Physical Society},
Title = {Necessary and Sufficient Condition for Quantum State-Independent Contextuality},
Url = {http://link.aps.org/doi/10.1103/PhysRevLett.114.250402},
Volume = {114},
Year = {2015},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.114.250402},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.114.250402}}
@article{Saha2015Quantum-nonloca,
Abstract = {Quantum nonlocality can be revealed "via local contextuality" in qudit-qudit entangled systems with d>2d > 2, that is, through the violation of inequalities containing only Alice-Bob correlations that admit a local description, and Alice-Alice correlations (between the results of sequences of measurements on Alice's subsystem) that admit a local (but contextual) description. A fundamental question to understand the respective roles of entanglement and local contextuality is whether nonlocality via local contextuality exists when the parties have only qubit-qubit entanglement. Here we respond affirmatively to this question. This result further clarifies the connection between contextuality and nonlocality and opens the door for observing nonlocality via local contextuality in actual experiments.},
Author = {Debashis Saha and Ad{\'a}n Cabello and Sujit K. Choudhary and Marcin Paw{\l}owski},
Citation_Arxiv_Id = {1507.08480},
Citation_Author = {Paw{\l}owski, Marcin},
Citation_Date = {2015/07/30},
Citation_Online_Date = {2015/07/30},
Citation_Pdf_Url = {http://arxiv.org/pdf/1507.08480},
Citation_Title = {Quantum nonlocality via local contextuality with qubit-qubit entanglement},
Date-Added = {2015-11-13 11:03:01 +0000},
Date-Modified = {2015-11-13 11:03:01 +0000},
Eprint = {arXiv:1507.08480},
Journal = {arXiv.org},
Title = {Quantum nonlocality via local contextuality with qubit-qubit entanglement},
Year = {2015},
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@article{Liang20111,
Abstract = {In 1960, the mathematician Ernst Specker described a simple example of nonclassical correlations, the counter-intuitive features of which he dramatized using a parable about a seer, who sets an impossible prediction task to his daughter's suitors. We revisit this example here, using it as an entr{\'e}e to three central concepts in quantum foundations: contextuality, Bell-nonlocality, and complementarity. Specifically, we show that Specker's parable offers a narrative thread that weaves together a large number of results, including the following: the impossibility of measurement-noncontextual and outcome-deterministic ontological models of quantum theory (the 1967 Kochen--Specker theorem), in particular, the recent state-specific pentagram proof of Klyachko; the impossibility of Bell-local models of quantum theory (Bell's theorem), especially the proofs by Mermin and Hardy and extensions thereof; the impossibility of a preparation-noncontextual ontological model of quantum theory; the existence of triples of positive operator valued measures (POVMs) that can be measured jointly pairwise but not triplewise. Along the way, several novel results are presented: a generalization of a theorem by Fine connecting the existence of a joint distribution over outcomes of counterfactual measurements to the existence of a measurement-noncontextual and outcome-deterministic ontological model; a generalization of Klyachko's proof of the Kochen--Specker theorem from pentagrams to a family of star polygons; a proof of the Kochen--Specker theorem in the style of Hardy's proof of Bell's theorem (i.e., one that makes use of the failure of the transitivity of implication for counterfactual statements); a categorization of contextual and Bell-nonlocal correlations in terms of frustrated networks; a derivation of a new inequality testing preparation noncontextuality; some novel results on the joint measurability of \{POVMs\} and the question of whether these can be modeled noncontextually. Finally, we emphasize that Specker's parable of the overprotective seer provides a novel type of foil to quantum theory, challenging us to explain why the particular sort of contextuality and complementarity embodied therein does not arise in a quantum world. },
Author = {Yeong-Cherng Liang and Robert W. Spekkens and Howard M. Wiseman},
Date-Added = {2015-11-13 10:29:44 +0000},
Date-Modified = {2015-11-13 10:29:44 +0000},
Doi = {http://dx.doi.org/10.1016/j.physrep.2011.05.001},
Issn = {0370-1573},
Journal = {Physics Reports},
Keywords = {Bell inequalities},
Number = {1--2},
Pages = {1 - 39},
Title = {Specker's parable of the overprotective seer: A road to contextuality, nonlocality and complementarity},
Url = {http://www.sciencedirect.com/science/article/pii/S0370157311001517},
Volume = {506},
Year = {2011},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0370157311001517},
Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.physrep.2011.05.001}}
@article{PhysRevLett.115.110403,
Author = {Kunjwal, Ravi and Spekkens, Robert W.},
Date-Added = {2015-11-13 10:26:37 +0000},
Date-Modified = {2015-11-13 10:26:37 +0000},
Doi = {10.1103/PhysRevLett.115.110403},
Issue = {11},
Journal = {Phys. Rev. Lett.},
Month = {Sep},
Numpages = {5},
Pages = {110403},
Publisher = {American Physical Society},
Title = {From the Kochen-Specker Theorem to Noncontextuality Inequalities without Assuming Determinism},
Url = {http://link.aps.org/doi/10.1103/PhysRevLett.115.110403},
Volume = {115},
Year = {2015},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.115.110403},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.115.110403}}
@article{Samson-Abramsky2015Contextuality-C,
Abstract = {Contextuality is a key feature of quantum mechanics that provides an important non-classical resource for quantum information and computation. Abramsky and Brandenburger used sheaf theory to give a general treatment of contextuality in quantum theory [New Journal of Physics 13 (2011) 113036]. However, contextual phenomena are found in other fields as well, for example database theory. In this paper, we shall develop this unified view of contextuality. We provide two main contributions: firstly, we expose a remarkable connection between contexuality and logical paradoxes; secondly, we show that an important class of contextuality arguments has a topological origin. More specifically, we show that "All-vs-Nothing" proofs of contextuality are witnessed by cohomological obstructions.},
Author = {Samson Abramsky and Rui Soares Barbosa and Kohei Kishida and Raymond Lal and Shane Mansfield},
Citation_Arxiv_Id = {1502.03097},
Citation_Author = {Mansfield, Shane},
Citation_Date = {2015/02/10},
Citation_Online_Date = {2015/02/10},
Citation_Pdf_Url = {http://arxiv.org/pdf/1502.03097},
Citation_Title = {Contextuality, Cohomology and Paradox},
Date-Added = {2015-11-13 10:14:07 +0000},
Date-Modified = {2015-11-13 10:14:07 +0000},
Eprint = {arXiv:1502.03097},
Journal = {arXiv.org},
Title = {Contextuality, Cohomology and Paradox},
Year = {2015},
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@article{Abramsky2015Hardy-is-almost,
Abstract = {We show that all nn-qubit entangled states, with the exception of tensor products of single-qubit and bipartite maximally-entangled states, admit Hardy-type proofs of non-locality without inequalities or probabilities. More precisely, we show that for all such states, there are local, one-qubit observables such that the resulting probability tables are logically contextual in the sense of Abramsky and Brandenburger, this being the general form of the Hardy-type property. Moreover, our proof is constructive: given a state, we show how to produce the witnessing local observables. In fact, we give an algorithm to do this. Although the algorithm is reasonably straightforward, its proof of correctness is non-trivial. A further striking feature is that we show that n+2n+2 local observables suffice to witness the logical contextuality of any nn-qubit state: two each for two for the parties, and one each for the remaining n−2n-2 parties.},
Author = {Samson Abramsky and Carmen M. Constantin and Shenggang Ying},
Citation_Arxiv_Id = {1506.01365},
Citation_Author = {Ying, Shenggang},
Citation_Date = {2015/06/03},
Citation_Online_Date = {2015/06/03},
Citation_Pdf_Url = {http://arxiv.org/pdf/1506.01365},
Citation_Title = {Hardy is (almost) everywhere: nonlocality without inequalities for almost all entangled multipartite states},
Date-Added = {2015-11-13 10:07:03 +0000},
Date-Modified = {2015-11-13 10:07:03 +0000},
Eprint = {arXiv:1506.01365},
Journal = {arXiv.org},
Title = {Hardy is (almost) everywhere: nonlocality without inequalities for almost all entangled multipartite states},
Year = {2015},
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@incollection{Mellies-2013-dialogfrobs,
Author = {Melli{\`e}s, Paul-Andr{\'e}},
Booktitle = {Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky},
Date-Added = {2015-10-20 13:22:10 +0000},
Date-Modified = {2015-10-20 13:22:33 +0000},
Doi = {10.1007/978-3-642-38164-5_15},
Editor = {Coecke, Bob and Ong, Luke and Panangaden, Prakash},
Isbn = {978-3-642-38163-8},
Language = {English},
Pages = {197-224},
Publisher = {Springer Berlin Heidelberg},
Series = {Lecture Notes in Computer Science},
Title = {Dialogue Categories and Frobenius Monoids},
Url = {http://dx.doi.org/10.1007/978-3-642-38164-5_15},
Volume = {7860},
Year = {2013},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-38164-5_15}}
@inproceedings{Kartsaklis2015A-Frobenius-Mod,
Abstract = {The categorical compositional distributional model of Coecke, Sadrzadeh and Clark provides a linguistically motivated procedure for computing the meaning of a sentence as a function of the distributional meaning of the words therein. The theoretical framework allows for reasoning about compositional aspects of language and offers structural ways of studying the underlying relationships. While the model so far has been applied on the level of syntactic structures, a sentence can bring extra information conveyed in utterances via intonational means. In the current paper we extend the framework in order to accommodate this additional information, using Frobenius algebraic structures canonically induced over the basis of finite-dimensional vector spaces. We detail the theory, provide truth-theoretic and distributional semantics for meanings of intonationally-marked utterances, and present justifications and extensive examples.},
Author = {Dimitri Kartsaklis and Mehrnoosh Sadrzadeh},
Booktitle = {Proceedings of 14th Meeting on Mathematics of Language},
Citation_Arxiv_Id = {1505.06294},
Citation_Author = {Sadrzadeh, Mehrnoosh},
Citation_Date = {2015/05/23},
Citation_Online_Date = {2015/05/23},
Citation_Pdf_Url = {http://arxiv.org/pdf/1505.06294},
Citation_Title = {A Frobenius Model of Information Structure in Categorical Compositional Distributional Semantics},
Date-Added = {2015-10-13 09:13:54 +0000},
Date-Modified = {2015-10-13 09:13:54 +0000},
Eprint = {arXiv:1505.06294},
Title = {A Frobenius Model of Information Structure in Categorical Compositional Distributional Semantics},
Year = {2015},
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@article{Balkir2015Distributional-,
Abstract = {Categorical compositional distributional model of Coecke et al. (2010) suggests a way to combine grammatical composition of the formal, type logical models with the corpus based, empirical word representations of distributional semantics. This paper contributes to the project by expanding the model to also capture entailment relations. This is achieved by extending the representations of words from points in meaning space to density operators, which are probability distributions on the subspaces of the space. A symmetric measure of similarity and an asymmetric measure of entailment is defined, where lexical entailment is measured using von Neumann entropy, the quantum variant of Kullback-Leibler divergence. Lexical entailment, combined with the composition map on word representations, provides a method to obtain entailment relations on the level of sentences.},
Author = {Esma Balkir and Mehrnoosh Sadrzadeh and Bob Coecke},
Citation_Arxiv_Id = {1506.06534},
Citation_Author = {Coecke, Bob},
Citation_Date = {2015/06/22},
Citation_Online_Date = {2015/06/22},
Citation_Pdf_Url = {http://arxiv.org/pdf/1506.06534},
Citation_Title = {Distributional Sentence Entailment Using Density Matrices},
Date-Added = {2015-10-13 09:10:54 +0000},
Date-Modified = {2015-10-13 09:10:54 +0000},
Eprint = {arXiv:1506.06534},
Journal = {arXiv.org},
Number = {1506.06534},
Title = {Distributional Sentence Entailment Using Density Matrices},
Year = {2015},
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@article{Jans:1959aa,
Author = {Jans, J. P.},
Date-Added = {2015-10-12 11:52:15 +0000},
Date-Modified = {2015-10-12 11:52:15 +0000},
Doi = {10.2307/1970189},
Journal = {Annals of Mathematics},
Month = {March},
Number = {2},
Pages = {392-407},
Title = {On Frobenius Algebras},
Volume = {69},
Year = {1959},
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Bdsk-Url-1 = {http://dx.doi.org/10.2307/1970189}}
@article{Cheng2011PSP8239257,
Abstract = {We give a framework for combining n monads on the same category via distributive laws satisfying Yang--Baxter equations, extending the classical result of Beck which combines two monads via one distributive law. We show that this corresponds to iterating n-times the process of taking the 2-category of monads in a 2-category, extending the result of Street characterising distributive laws. We show that this framework can be used to construct the free strict n-category monad on n-dimensional globular sets; we first construct for each i a monad for composition along bounding i-cells, and then we show that the interchange laws define distributive laws between these monads, satisfying the necessary Yang--Baxter equations.},
Author = {Eugenia Cheng},
Date-Added = {2015-10-11 23:40:48 +0000},
Date-Modified = {2015-10-11 23:58:38 +0000},
Doi = {10.1017/S0305004110000599},
Issn = {1469-8064},
Issue = {03},
Journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
Month = {5},
Numpages = {29},
Pages = {459--487},
Title = {Iterated distributive laws},
Url = {http://journals.cambridge.org/article_S0305004110000599},
Volume = {150},
Year = {2011},
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Bdsk-Url-1 = {http://journals.cambridge.org/article_S0305004110000599},
Bdsk-Url-2 = {http://dx.doi.org/10.1017/S0305004110000599}}
@incollection{Bruni:2011:captni,
Author = {Bruni, Roberto and Melgratti, Hern{\'a}n and Montanari, Ugo},
Booktitle = {CONCUR 2011 -- Concurrency Theory},
Date-Added = {2015-10-11 23:19:51 +0000},
Date-Modified = {2016-01-13 16:04:23 +0000},
Doi = {10.1007/978-3-642-23217-6_21},
Editor = {Katoen, Joost-Pieter and K{\"o}nig, Barbara},
Isbn = {978-3-642-23216-9},
Language = {English},
Pages = {312-326},
Publisher = {Springer Berlin Heidelberg},
Series = {Lecture Notes in Computer Science},
Title = {A Connector Algebra for {P/T} Nets Interactions},
Url = {http://dx.doi.org/10.1007/978-3-642-23217-6_21},
Volume = {6901},
Year = {2011},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-23217-6_21}}
@incollection{sobocinksi:2013:aa,
Abstract = {In recent work, the author and others have studied compositional algebras of Petri nets. Here we consider mathematical aspects of the pure linking algebras that underly them. We characterise composition of nets without places as the composition of spans over appropriate categories of relations, and study the underlying algebraic structures.},
Author = {Soboci{\'n}ski, Pawe{\l}},
Booktitle = {Algebra and Coalgebra in Computer Science},
Date-Added = {2015-10-11 23:16:46 +0000},
Date-Modified = {2015-10-11 23:17:01 +0000},
Doi = {10.1007/978-3-642-40206-7_21},
Editor = {Heckel, Reiko and Milius, Stefan},
Isbn = {978-3-642-40205-0},
Language = {English},
Pages = {282-298},
Publisher = {Springer Berlin Heidelberg},
Series = {Lecture Notes in Computer Science},
Title = {Nets, Relations and Linking Diagrams},
Url = {http://dx.doi.org/10.1007/978-3-642-40206-7_21},
Volume = {8089},
Year = {2013},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-40206-7_21}}
@inproceedings{Wang:2014aa,
Abstract = {We introduce a dichromatic calculus (RG) for qutrit systems. We show that the decomposition of the qutrit Hadamard gate is non-unique and not derivable from the dichromatic calculus. As an application of the dichromatic calculus, we depict a quantum algorithm with a single qutrit. Since it is not easy to decompose an arbitrary d by d unitary matrix into Z and X phase gates when d > 2, the proof of the universality of qudit ZX calculus for quantum mechanics is far from trivial. We construct a counterexample to Ranchin's universality proof, and give another proof by Lie theory that the qudit ZX calculus contains all single qudit unitary transformations, which implies that qudit ZX calculus, with qutrit dichromatic calculus as a special case, is universal for quantum mechanics.},
Author = {Quanlong Wang and Xiaoning Bian},
Booktitle = {Proceedings QPL 2014,},
Citation_Arxiv_Id = {1406.3056},
Citation_Author = {Bian, Xiaoning},
Citation_Date = {2014/06/08},
Citation_Doi = {10.4204/EPTCS.172.7},
Citation_Online_Date = {2014/12/30},
Citation_Pdf_Url = {http://arxiv.org/pdf/1406.3056},
Citation_Title = {Qutrit Dichromatic Calculus and Its Universality},
Date-Added = {2015-10-10 08:18:07 +0000},
Date-Modified = {2015-10-10 08:18:07 +0000},
Doi = {10.4204/EPTCS.172.7},
Eprint = {arXiv:1406.3056},
Pages = {92-101},
Series = {EPTCS},
Title = {Qutrit Dichromatic Calculus and Its Universality},
Volume = {172},
Year = {2014},
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@incollection{Coecke:2015aa,
Abstract = {This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular case, namely the study of complementarity and non-locality, two fundamental concepts of quantum theory whose relationship we explore in later part of this chapter. The diagrammatic calculus that we are concerned with here is not merely an illustrative tool, but it has both (i) a conceptual physical backbone, which allows it to act as a foundation for diverse physical theories, and (ii) a genuine mathematical underpinning, permitting one to relate it to standard mathematical structures.},
Author = {Bob Coecke and Ross Duncan and Aleks Kissinger and Quanlong Wang},
Booktitle = {Quantum Theory: Informational Foundations and Foils},
Citation_Arxiv_Id = {1506.03632},
Citation_Author = {Wang, Quanlong},
Citation_Date = {2015/06/11},
Citation_Online_Date = {2015/06/11},
Citation_Pdf_Url = {http://arxiv.org/pdf/1506.03632},
Citation_Title = {Generalised Compositional Theories and Diagrammatic Reasoning},
Date-Added = {2015-10-10 07:59:11 +0000},
Date-Modified = {2015-10-10 07:59:11 +0000},
Editor = {G. Chirabella and R. Spekkens},
Eprint = {arXiv:1506.03632},
Publisher = {Springer},
Title = {Generalised Compositional Theories and Diagrammatic Reasoning},
Year = {2015},
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@inproceedings{Heunen:2013aa,
Abstract = {The recently introduced CP*-construction unites quantum channels and classical systems, subsuming the earlier CPM-construction in categorical quantum mechanics. We compare this construction to two earlier attempts at solving this problem: freely adding biproducts to CPM, and freely splitting idempotents in CPM. The CP*-construction embeds the former, and embeds into the latter, but neither embedding is an equivalence in general.},
Author = {Chris Heunen and Aleks Kissinger and Peter Selinger},
Booktitle = {Proceedings QPL 2013},
Citation_Arxiv_Id = {1308.4557},
Citation_Author = {Selinger, Peter},
Citation_Date = {2013/08/21},
Citation_Doi = {10.4204/EPTCS.171.7},
Citation_Online_Date = {2014/12/30},
Citation_Pdf_Url = {http://arxiv.org/pdf/1308.4557},
Citation_Title = {Completely positive projections and biproducts},
Date-Added = {2015-10-10 07:52:56 +0000},
Date-Modified = {2015-10-10 07:52:56 +0000},
Doi = {10.4204/EPTCS.171.7},
Eprint = {arXiv:1308.4557},
Pages = {71-83},
Series = {EPTCS},
Title = {Completely positive projections and biproducts},
Volume = {171},
Year = {2013},
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Bdsk-Url-1 = {http://dx.doi.org/10.4204/EPTCS.171.7}}
@inproceedings{Ranchin:2014ab,
Abstract = {We generalize the ZX calculus to quantum systems of dimension higher than two. The resulting calculus is sound and universal for quantum mechanics. We define the notion of a mutually unbiased qudit theory and study two particular instances of these theories in detail: qudit stabilizer quantum mechanics and Spekkens-Schreiber toy theory for dits. The calculus allows us to analyze the structure of qudit stabilizer quantum mechanics and provides a geometrical picture of qudit stabilizer theory using D-toruses, which generalizes the Bloch sphere picture for qubit stabilizer quantum mechanics. We also use our framework to describe generalizations of Spekkens toy theory to higher dimensional systems. This gives a novel proof that qudit stabilizer quantum mechanics and Spekkens-Schreiber toy theory for dits are operationally equivalent in three dimensions. The qudit pictorial calculus is a useful tool to study quantum foundations, understand the relationship between qubit and qudit quantum mechanics, and provide a novel, high level description of quantum information protocols.},
Author = {Andr{\'e} Ranchin},
Booktitle = {Proceedings QPL 2014},
Citation_Arxiv_Id = {1404.1288},
Citation_Author = {Ranchin, Andr{\'e}},
Citation_Date = {2014/04/04},
Citation_Doi = {10.4204/EPTCS.172.6},
Citation_Online_Date = {2014/12/30},
Citation_Pdf_Url = {http://arxiv.org/pdf/1404.1288},
Citation_Title = {Depicting qudit quantum mechanics and mutually unbiased qudit theories},
Date-Added = {2015-10-10 07:48:05 +0000},
Date-Modified = {2015-10-10 07:48:05 +0000},
Doi = {10.4204/EPTCS.172.6},
Eprint = {arXiv:1404.1288},
Pages = {68-91},
Series = {EPTCS},
Title = {Depicting qudit quantum mechanics and mutually unbiased qudit theories},
Volume = {172},
Year = {2014},
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Bdsk-Url-1 = {http://dx.doi.org/10.4204/EPTCS.172.6}}
@article{Gogioso:2015ac,
Abstract = {The study of non-locality is fundamental to the understanding of quantum mechanics. The past 50 years have seen a number of non-locality proofs, but its fundamental building blocks, and the exact role it plays in quantum protocols, has remained elusive. In this paper, we focus on a particular flavour of non-locality, generalising Mermin's argument on the GHZ state. Using strongly complementary observables, we provide necessary and sufficient conditions for Mermin non-locality in abstract process theories. We show that the existence of more phases than classical points (aka eigenstates) is not sufficient, and that the key to Mermin non-locality lies in the presence of certain algebraically non-trivial phases. This allows us to show that fRel, a favourite toy model for categorical quantum mechanics, is Mermin local. We show Mermin non-locality to be the key resource ensuring the device-independent security of the HBB CQ (N,N) family of Quantum Secret Sharing protocols. Finally, we challenge the unspoken assumption that the measurements involved in Mermin-type scenarios should be complementary (like the pair X,Y), opening the doors to a much wider class of potential experimental setups than currently employed. In short, we give conditions for Mermin non-locality tests on any number of systems, where each party has an arbitrary number of measurement choices, where each measurement has an arbitrary number of outcomes and further, that works in any abstract process theory.},
Author = {Stefano Gogioso and William Zeng},
Citation_Arxiv_Id = {1506.02675},
Citation_Author = {Zeng, William},
Citation_Date = {2015/06/08},
Citation_Online_Date = {2015/08/14},
Citation_Pdf_Url = {http://arxiv.org/pdf/1506.02675},
Citation_Title = {Mermin Non-Locality in Abstract Process Theories},
Date-Added = {2015-10-10 07:45:28 +0000},
Date-Modified = {2015-10-10 07:45:28 +0000},
Eprint = {arXiv:1506.02675},
Journal = {submitted to New Journal of Physics},
Title = {Mermin Non-Locality in Abstract Process Theories},
Year = {2015},
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@inproceedings{Gogioso:2015ab,
Abstract = {Applying ideas from monadic dynamics to the well-established framework of categorical quantum mechanics, we provide a novel toolbox for the simulation of finite-dimensional quantum dynamics. We use strongly complementary structures to give a graphical characterisation of quantum clocks, their action on systems and the relevant energy observables, and we proceed to formalise the connection between unitary dynamics and projection-valued spectra. We identify the Weyl canonical commutation relations in the axioms of strong complementarity, and conclude the existence of a dual pair of time/energy observables for finite-dimensional quantum clocks, with the relevant uncertainty principle given by mutual unbias of the corresponding orthonormal bases. We show that Schr\"odinger's equation can be abstractly formulated as characterising the Fourier transforms of certain Eilenberg-Moore morphisms from a quantum clock to a quantum dynamical system, and we use this to obtain a generalised version of the Feynman's clock construction. We tackle the issue of synchronism of clocks and systems, prove conservation of total energy and give conditions for the existence of an internal time observable for a quantum dynamical system. Finally, we identify our treatment as part of a more general theory of simulated symmetries of quantum systems (of which our clock actions are a special case) and their conservation laws (of which energy is a special case).},
Author = {Stefano Gogioso},
Booktitle = {QPL 2015},
Citation_Arxiv_Id = {1501.06489},
Citation_Author = {Gogioso, Stefano},
Citation_Date = {2015/01/23},
Citation_Online_Date = {2015/02/25},
Citation_Pdf_Url = {http://arxiv.org/pdf/1501.06489},
Citation_Title = {Categorical Semantics for Schr\"odinger's Equation},
Date-Added = {2015-10-10 07:43:14 +0000},
Date-Modified = {2015-10-10 08:39:45 +0000},
Eprint = {arXiv:1501.06489},
Title = {Categorical Semantics for {S}chr{\"o}dinger's Equation},
Year = {2015},
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@article{Gogioso:2015aa,
Abstract = {Ongoing work in quantum information emphasises the need for a structural understanding of quantum speedups: in this work, we focus on the quantum Fourier transform and the structures in quantum theory that enable it. We elucidate a general connection in any process theory between the Fourier transform and strongly complementary observables, i.e. Hopf algebras in dagger symmetric monoidal categories. We generalise the necessary tools of representation theory from fdHilb to arbitrary dagger symmetric monoidal categories. We define groups, characters and representations, and we prove their relation to strong complementarity. The Fourier transform is then defined in terms of pairs of strongly complementary observables, in both the abelian and non-abelian case. In the abelian case, we draw the connection with Pontryagin duality and provide categorical proofs of the Fourier Inversion Theorem, the Convolution Theory, and Pontryagin duality. Our work finds application in the novel characterisation of the Fourier transform for the category fRel of finite sets and relations. This is a result of interest for the study of categorical quantum algorithms, as the usual construction of the quantum Fourier transform in terms of Fourier matrices is shown to fail in fRel. Despite this, the process theoretic perspective on the Fourier transform is sensible in this setting. Furthermore, our categorical setting provides a generalisation of the abelian Fourier transform from finite-dimensional Hilbert spaces to finite-dimensional modules over arbitrary semirings, as well as a further generalisation to finite non-abelian groups, including a fully categorical generalisation of the Gelfand-Naimark theorem.},
Author = {Stefano Gogioso and William Zeng},
Citation_Arxiv_Id = {1501.04995},
Citation_Author = {Zeng, William},
Citation_Date = {2015/01/19},
Citation_Online_Date = {2015/08/14},
Citation_Pdf_Url = {http://arxiv.org/pdf/1501.04995},
Citation_Title = {Fourier transforms from strongly complementary observables},
Date-Added = {2015-10-10 07:40:16 +0000},
Date-Modified = {2015-10-10 07:40:16 +0000},
Eprint = {arXiv:1501.04995},
Journal = {Sumbitted to Applied Categorical Structures},
Title = {Fourier transforms from strongly complementary observables},
Year = {2015},
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@inproceedings{Witt:2014aa,
Abstract = {We prove that the ZX-calculus is incomplete for quantum mechanics. We suggest the addition of a new 'color-swap' rule, of which currently no analytical formulation is known and which we suspect may be necessary, but not sufficient to make the ZX-calculus complete.},
Author = {Christian Schr{\"o}der de Witt and Vladimir Zamdzhiev},
Booktitle = {Proceedings QPL 2014},
Citation_Arxiv_Id = {1404.3633},
Citation_Author = {Zamdzhiev, Vladimir},
Citation_Date = {2014/04/14},
Citation_Doi = {10.4204/EPTCS.172.20},
Citation_Online_Date = {2014/12/30},
Citation_Pdf_Url = {http://arxiv.org/pdf/1404.3633},
Citation_Title = {The ZX-calculus is incomplete for quantum mechanics},
Date-Added = {2015-10-10 07:34:03 +0000},
Date-Modified = {2015-10-10 07:34:03 +0000},
Doi = {10.4204/EPTCS.172.20},
Eprint = {arXiv:1404.3633},
Pages = {285-292},
Series = {EPTCS},
Title = {The ZX-calculus is incomplete for quantum mechanics},
Volume = {172},
Year = {2014},
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Bdsk-Url-1 = {http://dx.doi.org/10.4204/EPTCS.172.20}}
@inproceedings{Backens:2015aa,
Abstract = {The ZX-calculus is a graphical language for quantum processes with built-in rewrite rules. The rewrite rules allow equalities to be derived entirely graphically, leading to the question of completeness: can any equality that is derivable using matrices also be derived graphically? The ZX-calculus is known to be complete for scalar-free pure qubit stabilizer quantum mechanics, meaning any equality between two pure stabilizer operators that is true up to a non-zero scalar factor can be derived using the graphical rewrite rules. Here, we replace those scalar-free rewrite rules with correctly scaled ones and show that, by adding one new diagram element and a new rewrite rule, the calculus can be made complete for pure qubit stabilizer quantum mechanics with scalars. This completeness property allows amplitudes and probabilities to be calculated entirely graphically. We also explicitly consider stabilizer zero diagrams, i.e. diagrams that represent a zero matrix, and show that two new rewrite rules suffice to make the calculus complete for those.},
Author = {Miriam Backens},
Booktitle = {QPL 2015},
Citation_Arxiv_Id = {1507.03854},
Citation_Author = {Backens, Miriam},
Citation_Date = {2015/07/14},
Citation_Online_Date = {2015/07/14},
Citation_Pdf_Url = {http://arxiv.org/pdf/1507.03854},
Citation_Title = {Making the stabilizer ZX-calculus complete for scalars},
Date-Added = {2015-10-10 07:14:08 +0000},
Date-Modified = {2015-10-10 07:14:08 +0000},
Eprint = {arXiv:1507.03854},
Title = {Making the stabilizer ZX-calculus complete for scalars},
Year = {2015},
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@inproceedings{Backens:2014aa,
Abstract = {The ZX-calculus is a graphical calculus for reasoning about pure state qubit quantum mechanics. It is complete for pure qubit stabilizer quantum mechanics, meaning any equality involving only stabilizer operations that can be derived using matrices can also be derived pictorially. Stabilizer operations include the unitary Clifford group, as well as preparation of qubits in the state |0>, and measurements in the computational basis. For general pure state qubit quantum mechanics, the ZX-calculus is incomplete: there exist equalities involving non-stabilizer unitary operations on single qubits which cannot be derived from the current rule set for the ZX-calculus. Here, we show that the ZX-calculus for single qubits remains complete upon adding the operator T to the single-qubit stabilizer operations. This is particularly interesting as the resulting single-qubit Clifford+T group is approximately universal, i.e. any unitary single-qubit operator can be approximated to arbitrary accuracy using only Clifford operators and T.},
Author = {Miriam Backens},
Booktitle = {Proceedings QPL 2014},
Citation_Arxiv_Id = {1412.8553},
Citation_Author = {Backens, Miriam},
Citation_Date = {2014/12/30},
Citation_Doi = {10.4204/EPTCS.172.21},
Citation_Online_Date = {2014/12/30},
Citation_Pdf_Url = {http://arxiv.org/pdf/1412.8553},
Citation_Title = {The ZX-calculus is complete for the single-qubit Clifford+T group},
Date-Added = {2015-10-10 07:12:25 +0000},
Date-Modified = {2015-10-10 08:34:19 +0000},
Doi = {10.4204/EPTCS.172.21},
Eprint = {arXiv:1412.8553},
Pages = {293-303},
Series = {EPTCS},
Title = {The ZX-calculus is complete for the single-qubit {C}lifford+{T} group},
Volume = {172},
Year = {2014},
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Bdsk-Url-1 = {http://dx.doi.org/10.4204/EPTCS.172.21}}
@article{backens:2015:aa,
Abstract = {While quantum theory cannot be described by a local hidden variable model, it is nevertheless possible to construct such models that exhibit features commonly associated with quantum mechanics. These models are also used to explore the question of \(\psi \)-ontic versus \(\psi \)-epistemic theories for quantum mechanics. Spekkens' toy theory is one such model. It arises from classical probabilistic mechanics via a limit on the knowledge an observer may have about the state of a system. The toy theory for the simplest possible underlying system closely resembles stabilizer quantum mechanics, a fragment of quantum theory which is efficiently classically simulable but also non-local. Further analysis of the similarities and differences between those two theories can thus yield new insights into what distinguishes quantum theory from classical theories, and \(\psi \)-ontic from \(\psi \)-epistemic theories. In this paper, we develop a graphical language for Spekkens' toy theory. Graphical languages offer intuitive and rigorous formalisms for the analysis of quantum mechanics and similar theories. To compare quantum mechanics and a toy model, it is useful to have similar formalisms for both. We show that our language fully describes Spekkens' toy theory and in particular, that it is complete: meaning any equality that can be derived using other formalisms can also be derived entirely graphically. Our language is inspired by a similar graphical language for quantum mechanics called the ZX-calculus. Thus Spekkens' toy bit theory and stabilizer quantum mechanics can be analysed and compared using analogous graphical formalisms.},
Author = {Backens, Miriam and Duman, Ali Nabi},
Date-Added = {2015-10-10 07:08:59 +0000},
Date-Modified = {2015-10-11 22:54:21 +0000},
Doi = {10.1007/s10701-015-9957-7},
Eprint = {arXiv:1411.1618},
Issn = {0015-9018},
Journal = {Foundations of Physics},
Keywords = {Quantum foundations; Spekkens' toy theory; Stabilizer quantum mechanics; Graphical calculus; Categorical quantum mechanics; Graph states; $$\psi $$ ψ -epistemic theory},
Language = {English},
Pages = {1-34},
Publisher = {Springer US},
Title = {A Complete Graphical Calculus for {S}pekkens' Toy Bit Theory},
Url = {http://dx.doi.org/10.1007/s10701-015-9957-7},
Year = {2015},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10701-015-9957-7}}
@article{1367-2630-16-9-093021,
Abstract = {The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics (QM), meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound , i.e. any equality that can be derived graphically can also be derived using matrix mechanics. Here, we show that the ZX-calculus is complete for pure qubit stabilizer QM, meaning any equality that can be derived using matrices can also be derived pictorially. The proof relies on bringing diagrams into a normal form based on graph states and local Clifford operations.},
Author = {Miriam Backens},
Date-Added = {2015-10-10 07:06:02 +0000},
Date-Modified = {2015-10-10 07:06:38 +0000},
Eprint = {arXiv:1307.7025},
Journal = {New Journal of Physics},
Number = {9},
Pages = {093021},
Title = {The ZX-calculus is complete for stabilizer quantum mechanics},
Url = {http://stacks.iop.org/1367-2630/16/i=9/a=093021},
Volume = {16},
Year = {2014},
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Bdsk-Url-1 = {http://stacks.iop.org/1367-2630/16/i=9/a=093021}}
@article{andruskiewitch:2009:aa,
Author = {Andruskiewitsch, Nicol{\'a}s and Ferrer Santos, Walter},
Date-Added = {2015-10-10 06:36:24 +0000},
Date-Modified = {2015-10-10 08:33:54 +0000},
Doi = {10.1007/s10440-008-9393-1},
Eprint = {arXiv:0901.2460},
Issn = {0167-8019},
Journal = {Acta Applicandae Mathematicae},
Keywords = {Hopf algebras},
Language = {English},
Number = {1},
Pages = {3-17},
Publisher = {Springer Netherlands},
Title = {The Beginnings of the Theory of {H}opf Algebras},
Url = {http://dx.doi.org/10.1007/s10440-008-9393-1},
Volume = {108},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10440-008-9393-1}}
@incollection{Bertfried:2013aa,
Abstract = {Frobenius algebras surface at many places in mathematics and physics. Quite recently, using a convenient graphical notation, Frobenius algebras have been used to investigate foundational issues of quantum theory--- references will be given below. Also, as shown elsewhere in this book, Frobenius algebras emerge in the semantic analysis of natural languages. The aim of this chapter is to present the basic results of Frobenius algebras and their relation to finite-dimensional Hopf algebras, with special emphasis on use of graphical notation. Frobenius structures, which are related to ring theory, need to be considered too. Frobenius structures encode such notions as semi-simplicity and separability of rings. We occasionally need to extend the graphical calculus to encode properties of underlying rings, but will not venture properly into 2-categorical notions. Moreover, no new results may be found in this chapter, and far from everything that is known about the subject is covered here. However, in passing we will give some pointers to the literature, which unfortunately is far too large to be considered completely.},
Author = {Bertfried Fauser},
Booktitle = {Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse},
Date-Added = {2015-10-10 06:32:11 +0000},
Date-Modified = {2015-10-11 23:25:27 +0000},
Doi = {10.1093/acprof:oso/9780199646296.003.0002},
Editor = {Chris Heunen and Mehrnoosh Sadrzadeh and Edward Grefenstette},
Eprint = {arXiv:1202.6380},
Keywords = {frobenius algebras, graphical notation, hopf algebras, rings, quantum groups},
Publisher = {Oxford},
Title = {Some Graphical Aspects of {F}robenius Algebras},
Viewport = {width=device-width, minimum-scale=1.0, initial-scale=1.0},
Year = {2013},
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Bdsk-Url-1 = {http://dx.doi.org/10.1093/acprof:oso/9780199646296.003.0002}}
@inproceedings{4276577,
Abstract = {A novel, general approach is proposed to proving the compositionality of process equivalences on languages defined by structural operational semantics (SOS). The approach, based on modal logic, is inspired by the simple observation that if the set of formulas satisfied by a process can be derived from the corresponding sets for its subprocesses, then the logical equivalence is a congruence. Striving for generality, SOS rules are modeled categorically as bialgebraic distributive laws for some notions of process syntax and behaviour, and modal logics are modeled via coalgebraic polyadic modal logic. Compositionality is proved by providing a suitable notion of behaviour for the logic together with a dual distributive law, reflecting the one modeling the SOS specification. Concretely, the dual laws may appear as SOS-like rules where logical formulas play the role of processes, and their behaviour models logical decomposition over process syntax. The approach can be used either to proving compositionality for specific languages or for defining SOS congruence formats.},
Author = {Klin, B.},
Booktitle = {Logic in Computer Science, 2007. LICS 2007. 22nd Annual IEEE Symposium on},
Date-Added = {2015-10-10 06:18:32 +0000},
Date-Modified = {2015-10-10 06:18:32 +0000},
Doi = {10.1109/LICS.2007.13},
Issn = {1043-6871},
Keywords = {process algebra;programming language semantics;bialgebraic operational semantics;coalgebraic polyadic modal logic;logical equivalence;process equivalences compositionality;structural operational semantics;Algebra;Computer languages;Computer science;Context modeling;Joining processes;Logic functions;Power system modeling;Testing},
Month = {July},
Pages = {336-345},
Title = {Bialgebraic Operational Semantics and Modal Logic},
Year = {2007},
Bdsk-Url-1 = {http://dx.doi.org/10.1109/LICS.2007.13}}
@inproceedings{5230577,
Abstract = {Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order prepositional logic. One of the main difficulties that has to be faced during the elaboration of this kind of semantics is to characterize definable strategies, that is strategies which actually behave like a proof. This is usually done by restricting the model to strategies satisfying subtle combinatorial conditions, whose preservation under composition is often difficult to show. Here, we present an original methodology to achieve this task, which requires to combine advanced tools from game semantics, rewriting theory and categorical algebra. We introduce a diagrammatic presentation of the monoidal category of definable strategies of our model, by the means of generators and relations: those strategies can be generated from a finite set of atomic strategies and the equality between strategies admits a finite axiomatization, this equational structure corresponding to a polarized variation of the notion of bialgebra. This work thus bridges algebra and denotational semantics in order to reveal the structure of dependencies induced by first-order quantifiers, and lays the foundations for a mechanized analysis of causality in programming languages.},
Author = {Mimram, S.},
Booktitle = {Logic In Computer Science, 2009. LICS '09. 24th Annual IEEE Symposium on},
Date-Added = {2015-10-10 06:16:33 +0000},
Date-Modified = {2015-10-28 10:38:44 +0000},
Doi = {10.1109/LICS.2009.19},
Issn = {1043-6871},
Keywords = {category theory;group theory;process algebra;program diagnostics;programming language semantics;rewriting systems;theorem proving;categorical algebra;combinatorial condition;diagrammatic presentation;finite axiomatization;first-order causality structure;first-order prepositional logic;first-order quantifier;game semantics;monoidal category;programming language analysis;proof interactive behavior;rewriting theory;Algebra;Computer languages;Computer science;Equations;Game theory;Logic;Polarization;bialgebra;game semantics;polygraph;presentation of a category},
Month = {Aug},
Pages = {212-221},
Title = {The Structure of First-Order Causality},
Year = {2009},
Bdsk-Url-1 = {http://dx.doi.org/10.1109/LICS.2009.19}}
@article{MSC:7984430,
Abstract = { ABSTRACT Game semantics describe the interactive behaviour of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order propositional logic. One of the main difficulties that has to be faced during the elaboration of this kind of semantics is to characterise definable strategies, that is, strategies that actually behave like a proof. This is usually done by restricting the model to strategies satisfying subtle combinatorial conditions, whose preservation under composition is often difficult to show. In this paper we present an original methodology to achieve this task, which requires a combination of advanced tools from game semantics, rewriting theory and categorical algebra. We introduce a diagrammatic presentation of the monoidal category of definable strategies of our model using generators and relations: these strategies can be generated from a finite set of atomic strategies, and the equality between strategies admits a finite axiomatisation, and this equational structure corresponds to a polarised variation of the bialgebra notion. The work described in this paper thus forms a bridge between algebra and denotational semantics in order to reveal the structure of dependencies induced by first-order quantifiers, and lays the foundations for a mechanised analysis of causality in programming languages. },
Author = {Mimram, Samuel},
Date-Added = {2015-10-10 06:00:18 +0000},
Date-Modified = {2015-10-10 06:01:56 +0000},
Doi = {10.1017/S0960129510000459},
Eprint = {arXiv:0908.3994},
Issn = {1469-8072},
Issue = {01},
Journal = {Mathematical Structures in Computer Science},
Month = {2},
Numpages = {46},
Pages = {65--110},
Title = {The structure of first-order causality},
Url = {http://journals.cambridge.org/article_S0960129510000459},
Volume = {21},
Year = {2011},
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Bdsk-Url-1 = {http://journals.cambridge.org/article_S0960129510000459},
Bdsk-Url-2 = {http://dx.doi.org/10.1017/S0960129510000459}}
@incollection{Benson:1988:aa,
Author = {Benson, David B.},
Booktitle = {Mathematical Foundations of Programming Language Semantics},
Date-Added = {2015-10-10 05:55:23 +0000},
Date-Modified = {2015-10-10 05:55:50 +0000},
Doi = {10.1007/3-540-19020-1_32},
Editor = {Main, M. and Melton, A. and Mislove, M. and Schmidt, D.},
Isbn = {978-3-540-19020-2},
Language = {English},
Pages = {616-637},
Publisher = {Springer Berlin Heidelberg},
Series = {Lecture Notes in Computer Science},
Title = {The shuffle bialgebra},
Url = {http://dx.doi.org/10.1007/3-540-19020-1_32},
Volume = {298},
Year = {1988},
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@incollection{Worthington:2009:aa,
Author = {Worthington, James},
Booktitle = {Logical Foundations of Computer Science},
Date-Added = {2015-10-10 05:42:15 +0000},
Date-Modified = {2015-10-10 05:43:18 +0000},
Doi = {10.1007/978-3-540-92687-0_31},
Editor = {Artemov, Sergei and Nerode, Anil},
Eprint = {arXiv:0807.4553},
Isbn = {978-3-540-92686-3},
Pages = {451-467},
Publisher = {Springer Berlin Heidelberg},
Series = {Lecture Notes in Computer Science},
Title = {A Bialgebraic Approach to Automata and Formal Language Theory},
Url = {http://dx.doi.org/10.1007/978-3-540-92687-0_31},
Volume = {5407},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-540-92687-0_31}}
@article{sadrzadeh2014frobenius,
Author = {Sadrzadeh, Mehrnoosh and Clark, Stephen and Coecke, Bob},
Date-Added = {2015-10-10 04:34:54 +0000},
Date-Modified = {2016-01-13 16:02:56 +0000},
Journal = {Journal of Logic and Computation},
Publisher = {Oxford University Press},
Title = {The {F}robenius anatomy of word meanings II: possessive relative pronouns},
Year = {2014},
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@article{sadrzadeh2013frobenius,
Author = {Sadrzadeh, Mehrnoosh and Clark, Stephen and Coecke, Bob},
Date-Added = {2015-10-10 04:32:36 +0000},
Date-Modified = {2015-10-10 08:40:28 +0000},
Journal = {Journal of Logic and Computation},
Number = {6},
Pages = {1293--1317},
Publisher = {Oxford University Press},
Title = {The {F}robenius anatomy of word meanings I: subject and object relative pronouns},
Volume = {23},
Year = {2013},
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@article{Brandao:2015aa,
Abstract = {Quantum Darwinism posits that only specific information about a quantum system that is redundantly proliferated to many parts of its environment becomes accessible and objective, leading to the emergence of classical reality. However, it is not clear under what conditions this mechanism holds true. Here we prove that the emergence of classical features along the lines of quantum Darwinism is a general feature of any quantum dynamics: observers who acquire information indirectly through the environment have effective access at most to classical information about one and the same measurement of the quantum system. Our analysis does not rely on a strict conceptual splitting between a system-of-interest and its environment, and allows one to interpret any system as part of the environment of any other system. Finally, our approach leads to a full operational characterization of quantum discord in terms of local redistribution of correlations.},
Annote = {Supplementary information available for this article at http://www.nature.com/ncomms/2015/150812/ncomms8908/suppinfo/ncomms8908{\_}S1.html},
Author = {Brandao, Fernando G. S. L. and Piani, Marco and Horodecki, Pawel},
Date = {2015/08/12/online},
Date-Added = {2015-10-09 14:06:56 +0000},
Date-Modified = {2015-10-09 14:45:26 +0000},
Day = {12},
Eprint = {http://arxiv.org/abs/1310.8640},
Journal = {Nat Commun},
L3 = {10.1038/ncomms8908},
M3 = {Article},
Month = {08},
Publisher = {Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
Title = {Generic emergence of classical features in quantum Darwinism},
Ty = {JOUR},
Url = {http://dx.doi.org/10.1038/ncomms8908},
Volume = {6},
Year = {2015},
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Bdsk-Url-1 = {http://dx.doi.org/10.1038/ncomms8908}}
@book{street2007quantum,
Author = {Street, R.},
Date-Added = {2015-09-30 10:00:14 +0000},
Date-Modified = {2015-09-30 10:00:28 +0000},
Isbn = {9780521695244},
Lccn = {2007273697},
Publisher = {Cambridge University Press},
Series = {Australian Mathematical Society Lecture Series},
Title = {Quantum Groups: A Path to Current Algebra},
Year = {2007}}
@incollection{banach:1996:aa,
Author = {Banach, R.},
Booktitle = {Graph Grammars and Their Application to Computer Science},
Date-Added = {2015-09-22 11:37:17 +0000},
Date-Modified = {2015-09-22 11:37:54 +0000},
Doi = {10.1007/3-540-61228-9_76},
Editor = {Cuny, Janice and Ehrig, Hartmut and Engels, Gregor and Rozenberg, Grzegorz},
Isbn = {978-3-540-61228-5},
Keywords = {rewriting},
Language = {English},
Pages = {16-26},
Publisher = {Springer Berlin Heidelberg},
Series = {Lecture Notes in Computer Science},
Title = {The contractum in algebraic graph rewriting},
Url = {http://dx.doi.org/10.1007/3-540-61228-9_76},
Volume = {1073},
Year = {1996},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/3-540-61228-9_76}}
@incollection{bauderon:1996:aa,
Author = {Bauderon, Michel},
Booktitle = {Graph Grammars and Their Application to Computer Science},
Date-Added = {2015-09-22 11:35:29 +0000},
Date-Modified = {2015-09-22 11:37:59 +0000},
Doi = {10.1007/3-540-61228-9_77},
Editor = {Cuny, Janice and Ehrig, Hartmut and Engels, Gregor and Rozenberg, Grzegorz},
Isbn = {978-3-540-61228-5},
Keywords = {rewriting},
Language = {English},
Pages = {27-37},
Publisher = {Springer Berlin Heidelberg},
Series = {Lecture Notes in Computer Science},
Title = {A category-theoretical approach to vertex replacement: The generation of infinite graphs},
Url = {http://dx.doi.org/10.1007/3-540-61228-9_77},
Volume = {1073},
Year = {1996},
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@inproceedings{clerc_et_al:LIPIcs:2015:5191,
Address = {Dagstuhl, Germany},
Annote = {Keywords: presentation of a category, quotient category, localization, residuation},
Author = {Florence Clerc and Samuel Mimram},
Booktitle = {26th International Conference on Rewriting Techniques and Applications (RTA 2015)},
Date-Added = {2015-09-11 16:38:34 +0000},
Date-Modified = {2015-09-11 16:38:55 +0000},
Doi = {http://dx.doi.org/10.4230/LIPIcs.RTA.2015.89},
Editor = {Maribel Fern{\'a}ndez},
Isbn = {978-3-939897-85-9},
Issn = {1868-8969},
Keywords = {rewriting},
Pages = {89--105},
Publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
Series = {Leibniz International Proceedings in Informatics (LIPIcs)},
Title = {{Presenting a Category Modulo a Rewriting System}},
Url = {http://drops.dagstuhl.de/opus/volltexte/2015/5191},
Urn = {urn:nbn:de:0030-drops-51916},
Volume = {36},
Year = {2015},
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Bdsk-Url-2 = {http://dx.doi.org/10.4230/LIPIcs.RTA.2015.89}}
@article{Mimram:2014aa,
Abstract = {String rewriting systems have proved very useful to study monoids. In good cases, they give finite presentations of monoids, allowing computations on those and their manipulation by a computer. Even better, when the presentation is confluent and terminating, they provide one with a notion of canonical representative of the elements of the presented monoid. Polygraphs are a higher-dimensional generalization of this notion of presentation, from the setting of monoids to the much more general setting of n-categories. One of the main purposes of this article is to give a progressive introduction to the notion of higher-dimensional rewriting system provided by polygraphs, and describe its links with classical rewriting theory, string and term rewriting systems in particular. After introducing the general setting, we will be interested in proving local confluence for polygraphs presenting 2-categories and introduce a framework in which a finite 3-dimensional rewriting system admits a finite number of critical pairs.},
Author = {Samuel Mimram},
Date-Added = {2015-09-11 16:36:35 +0000},
Date-Modified = {2015-09-11 16:37:47 +0000},
Doi = {10.2168/LMCS-10(2:1)2014},
Journal = {Logical Methods in Computer Science},
Keywords = {rewriting},
Number = {2},
Pages = {1--47},
Title = {Towards 3-Dimensional Rewriting Theory},
Volume = {10},
Year = {2014},
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Bdsk-Url-1 = {http://dx.doi.org/10.2168/LMCS-10(2:1)2014}}
@unpublished{Mimram:2013aa,
Author = {Samuel Mimram},
Date-Added = {2015-09-11 16:34:25 +0000},
Date-Modified = {2015-09-11 16:34:25 +0000},
Title = {Representing 2-Dimensional Critical Pairs},
Year = {2013},
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@inproceedings{Hoch:2015aa,
Abstract = {Many optimization problems can be naturally represented as (hyper) graphs, where vertices correspond to variables and edges to tasks, whose cost depends on the values of the adjacent variables. Capitalizing on the structure of the graph, suitable dynamic programming strategies can select certain orders of evaluation of the variables which guarantee to reach both an optimal solution and a minimal size of the tables computed in the optimization process. In this paper we introduce a simple algebraic specification with parallel composition and restriction whose terms up to structural axioms are the graphs mentioned above. In addition, free (unrestricted) vertices are labelled with variables, and the specification includes operations of name permutation with finite support. We show a correspondence between the well-known tree decompositions of graphs and our terms. If an axiom of scope extension is dropped, several (hierarchical) terms actually correspond to the same graph. A suitable graphical structure can be found, corresponding to every hierarchical term. Evaluating such a graphical structure in some target algebra yields a dynamic programming strategy. If the target algebra satisfies the scope extension axiom, then the result does not depend on the particular structure, but only on the original graph. We apply our approach to the parking optimization problem developed in the ASCENS e-mobility case study, in collaboration with Volkswagen. Dynamic programming evaluations are particularly interesting for autonomic systems, where actual behavior often consists of propagating local knowledge to obtain global knowledge and getting it back for local decisions.},
Author = {Nicklas Hoch and Ugo Montanari and Matteo Sammartino},
Booktitle = {Proceedings GaM 2015},
Citation_Arxiv_Id = {1504.02613},
Citation_Author = {Sammartino, Matteo},
Citation_Date = {2015/04/10},
Citation_Doi = {10.4204/EPTCS.181.6},
Citation_Online_Date = {2015/04/10},
Citation_Pdf_Url = {http://arxiv.org/pdf/1504.02613},
Citation_Title = {Dynamic Programming on Nominal Graphs},
Date-Added = {2015-09-11 16:15:26 +0000},
Date-Modified = {2015-09-11 16:15:26 +0000},
Doi = {10.4204/EPTCS.181.6},
Eprint = {arXiv:1504.02613},
Pages = {80-96},
Series = {EPTCS},
Title = {Dynamic Programming on Nominal Graphs},
Volume = {181},
Year = {2015},
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Bdsk-Url-1 = {http://dx.doi.org/10.4204/EPTCS.181.6}}
@incollection{KZ:2015:aa,
Author = {Kissinger, Aleks and Zamdzhiev, Vladimir},
Booktitle = {Graph Transformation},
Date-Added = {2015-09-11 16:08:13 +0000},
Date-Modified = {2015-09-11 16:08:35 +0000},
Doi = {10.1007/978-3-319-21145-9_9},
Editor = {Parisi-Presicce, Francesco and Westfechtel, Bernhard},
Isbn = {978-3-319-21144-2},
Language = {English},
Pages = {138-154},
Publisher = {Springer International Publishing},
Series = {Lecture Notes in Computer Science},
Title = {Equational Reasoning with Context-Free Families of String Diagrams},
Url = {http://dx.doi.org/10.1007/978-3-319-21145-9_9},
Volume = {9151},
Year = {2015},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-319-21145-9_9}}
@article{Power1999102,
Abstract = {We give a systematic treatment of distributivity for a monad and a comonad as arises in incorporating category theoretic accounts of operational and denotational semantics, and in giving an intensional denotational semantics. We do this axiomatically, in terms of a monad and a comonad in a 2-category, giving accounts of the Eilenberg-Moore and Kleisli constructions. We analyse the eight possible relationships, deducing that two pairs are isomorphic, but that the other pairs are all distinct. We develop those 2-categorical definitions necessary to support this analysis. },
Author = {John Power and Hiroshi Watanabe},
Date-Added = {2015-09-08 15:56:26 +0000},
Date-Modified = {2015-09-08 15:56:26 +0000},
Doi = {http://dx.doi.org/10.1016/S1571-0661(05)80271-3},
Issn = {1571-0661},
Journal = {Electronic Notes in Theoretical Computer Science},
Note = {CMCS'99, Coalgebraic Methods in Computer Science},
Pages = {102 -},
Title = {Distributivity for a monad and a comonad},
Url = {http://www.sciencedirect.com/science/article/pii/S1571066105802713},
Volume = {19},
Year = {1999},
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@article{Lack2002243,
Abstract = {We give an explicit description of the free completion EM(K) of a 2-category K under the Eilenberg--Moore construction, and show that this has the same underlying category as the 2-category Mnd(K) of monads in K. We then demonstrate that much of the formal theory of monads can be deduced using only the universal property of this completion, provided that one is willing to work with EM(K) as the 2-category of monads rather than Mnd(K). We also introduce the wreaths in K; these are the objects of EM(EM(K)), and are to be thought of as generalized distributive laws. We study these wreaths, and give examples to show how they arise in a variety of contexts. },
Author = {Stephen Lack and Ross Street},
Date-Added = {2015-09-08 15:55:31 +0000},
Date-Modified = {2015-09-08 15:55:31 +0000},
Doi = {http://dx.doi.org/10.1016/S0022-4049(02)00137-8},
Issn = {0022-4049},
Journal = {Journal of Pure and Applied Algebra},
Note = {Special Volume celebrating the 70th birthday of Professor Max Kelly},
Number = {1--3},
Pages = {243 - 265},
Title = {The formal theory of monads \{II\}},
Url = {http://www.sciencedirect.com/science/article/pii/S0022404902001378},
Volume = {175},
Year = {2002},
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@article{Street1972149,
Author = {Ross Street},
Date-Added = {2015-09-08 15:53:52 +0000},
Date-Modified = {2015-09-08 15:53:52 +0000},
Doi = {http://dx.doi.org/10.1016/0022-4049(72)90019-9},
Issn = {0022-4049},
Journal = {Journal of Pure and Applied Algebra},
Number = {2},
Pages = {149 - 168},
Title = {The formal theory of monads},
Url = {http://www.sciencedirect.com/science/article/pii/0022404972900199},
Volume = {2},
Year = {1972},
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@article{Power2002137,
Abstract = {We give a systematic treatment of distributivity for a monad and a comonad as arises in giving category theoretic accounts of operational and denotational semantics, and in giving an intensional denotational semantics. We do this axiomatically, in terms of a monad and a comonad in a 2-category, giving accounts of the Eilenberg--Moore and Kleisli constructions. We analyse the eight possible relationships, deducing that two pairs are isomorphic, but that the other pairs are all distinct. We develop those 2-categorical definitions necessary to support this analysis. },
Author = {John Power and Hiroshi Watanabe},
Date-Added = {2015-09-08 15:51:51 +0000},
Date-Modified = {2015-09-08 15:51:51 +0000},
Doi = {http://dx.doi.org/10.1016/S0304-3975(01)00024-X},
Issn = {0304-3975},
Journal = {Theoretical Computer Science},
Keywords = {Bialgebra},
Note = {Coalgebraic Methods in Computer Science},
Number = {1--2},
Pages = {137 - 162},
Title = {Combining a monad and a comonad},
Url = {http://www.sciencedirect.com/science/article/pii/S030439750100024X},
Volume = {280},
Year = {2002},
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Bdsk-Url-2 = {http://dx.doi.org/10.1016/S0304-3975(01)00024-X}}
@article{Uustalu2008263,
Abstract = {We argue that symmetric (semi)monoidal comonads provide a means to structure context-dependent notions of computation such as notions of dataflow computation (computation on streams) and of tree relabelling as in attribute evaluation. We propose a generic semantics for extensions of simply typed lambda calculus with context-dependent operations analogous to the Moggi-style semantics for effectful languages based on strong monads. This continues the work in the early 90s by Brookes, Geva and Van Stone on the use of computational comonads in intensional semantics. },
Author = {Tarmo Uustalu and Varmo Vene},
Date-Added = {2015-09-08 15:49:14 +0000},
Date-Modified = {2015-09-08 15:49:14 +0000},
Doi = {http://dx.doi.org/10.1016/j.entcs.2008.05.029},
Issn = {1571-0661},
Journal = {Electronic Notes in Theoretical Computer Science},
Keywords = {coKleisli semantics},
Note = {Proceedings of the Ninth Workshop on Coalgebraic Methods in Computer Science (CMCS 2008)},
Number = {5},
Pages = {263 - 284},
Title = {Comonadic Notions of Computation},
Url = {http://www.sciencedirect.com/science/article/pii/S1571066108003435},
Volume = {203},
Year = {2008},
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Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.entcs.2008.05.029}}
@article{Rosebrugh:2004aa,
Abstract = {We show that the generic symmetric monoidal category with a commutative separable algebra which has a $\Sigma$-family of actions is the category of cospans of finite $\Sigma$-labelled graphs restricted to finite sets as objects, thus providing a syntax for automata on the alphabet $\Sigma$. We use this result to produce semantic functors for $\Sigma$-automata.},
Author = {R. Rosebrugh and N. Sabadini and R.F.C. Walters},
Date-Added = {2015-09-04 08:09:29 +0000},
Date-Modified = {2015-09-04 10:05:23 +0000},
Journal = {Theory and Applications of Categories (Special Issue for {CT}2004)},
Number = {6},
Pages = {164-177},
Title = {Generic commutative separable algebras and cospans of graphs},
Volume = {15},
Year = {2005},
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@article{Hyland:1993aa,
Author = {Hyland, M. and Ong, Luke},
Date-Added = {2015-09-01 11:10:54 +0000},
Date-Modified = {2015-09-01 11:12:12 +0000},
Journal = {Draft},
Title = {Fair Games and Full Completeness for Multiplicative Linear Logic without the MIX-Rule},
Year = {1993},
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@techreport{Bonchi2014a,
Author = {F. Bonchi and P. Soboci\'{n}ski and F. Zanasi},
Date-Added = {2015-07-27 10:48:08 +0000},
Date-Modified = {2015-10-10 08:35:04 +0000},
Institution = {arXiv:1403.7048},
Title = {Interacting {H}opf Algebras},
Url = {http://arxiv.org/abs/1403.7048},
Year = {2014},
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Bdsk-Url-1 = {http://arxiv.org/abs/1403.7048}}
@inproceedings{Bonchi2014,
Author = {F. Bonchi and P. Soboci\'{n}ski and F. Zanasi},
Booktitle = {FoSSaCS `14},
Date-Added = {2015-07-27 10:46:36 +0000},
Date-Modified = {2015-10-10 08:35:11 +0000},
Timestamp = {31.12.13},
Title = {Interacting Bialgebras are {F}robenius},
Url = {http://users.ecs.soton.ac.uk/~ps/papers/ib.pdf},
Year = {2014},
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@inproceedings{Kissinger:2015aa,
Abstract = {Equational reasoning with string diagrams provides an intuitive means of proving equations between morphisms in a symmetric monoidal category. This can be extended to proofs of infinite families of equations using a simple graphical syntax called !-box notation. While this does greatly increase the proving power of string diagrams, previous attempts to go beyond equational reasoning have been largely ad hoc, owing to the lack of a suitable logical framework for diagrammatic proofs involving !-boxes. In this paper, we extend equational reasoning with !-boxes to a fully-fledged first order logic called with conjunction, implication, and universal quantification over !-boxes. This logic, called !L, is then rich enough to properly formalise an induction principle for !-boxes. We then build a standard model for !L and give an example proof of a theorem for non-commutative bialgebras using !L, which is unobtainable by equational reasoning alone.},
Author = {Aleks Kissinger and David Quick},
Booktitle = {6th Conference on Algebra and Coalgebra in Computer Science (CALCO 2015)},
Date-Added = {2015-07-24 09:42:52 +0000},
Date-Modified = {2017-02-07 22:39:50 +0000},
Doi = {10.4230/LIPIcs.CALCO.2015.171},
Editor = {Lawrence S. Moss and Pawel Sobocinski},
Eprint = {arXiv:1505.00343},
Pages = {171--189},
Publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
Series = {Leibniz International Proceedings in Informatics (LIPIcs)},
Title = {A First-Order Logic for String Diagrams},
Volume = {35},
Year = {2015},
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Bdsk-Url-1 = {http://dx.doi.org/10.4230/LIPIcs.CALCO.2015.171}}
@incollection{Heunen:2013:l2,
Author = {Heunen, Chris},
Booktitle = {Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky},
Date-Added = {2015-06-18 15:00:00 +0000},
Date-Modified = {2015-06-18 15:00:36 +0000},
Doi = {10.1007/978-3-642-38164-5_8},
Editor = {Coecke, Bob and Ong, Luke and Panangaden, Prakash},
Isbn = {978-3-642-38163-8},
Language = {English},
Pages = {107-121},
Publisher = {Springer Berlin Heidelberg},
Series = {Lecture Notes in Computer Science},
Title = {On the Functor ℓ2},
Url = {http://dx.doi.org/10.1007/978-3-642-38164-5_8},
Volume = {7860},
Year = {2013},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-38164-5_8}}
@article{Heunen2013114,
Abstract = {We functorially characterize groupoids as special dagger Frobenius algebras in the category of sets and relations. This is then generalized to a non-unital setting, by establishing an adjunction between H*-algebras in the category of sets and relations, and locally cancellative regular semigroupoids. Finally, we study a universal passage from the former setting to the latter. },
Author = {Chris Heunen and Ivan Contreras and Alberto S. Cattaneo},
Date-Added = {2015-06-18 14:58:05 +0000},
Date-Modified = {2015-06-18 14:58:35 +0000},
Doi = {http://dx.doi.org/10.1016/j.jpaa.2012.04.002},
Eprint = {arXiv:1112.1284},
Issn = {0022-4049},
Journal = {Journal of Pure and Applied Algebra},
Number = {1},
Pages = {114 - 124},
Title = {Relative Frobenius algebras are groupoids},
Url = {http://www.sciencedirect.com/science/article/pii/S0022404912001284},
Volume = {217},
Year = {2013},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0022404912001284},
Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.jpaa.2012.04.002}}
@article{Heunen:2012:complementarity,
Author = {Heunen, Chris},
Date-Added = {2015-06-18 14:43:55 +0000},
Date-Modified = {2015-06-18 14:44:16 +0000},
Doi = {10.1007/s10701-011-9585-9},
Issn = {0015-9018},
Journal = {Foundations of Physics},
Keywords = {Complementarity; Dagger kernel monoidal category; Classical structure; Orthonormal basis; Orthomodular lattice; Boolean lattice; von Neumann algebra},
Language = {English},
Number = {7},
Pages = {856-873},
Publisher = {Springer US},
Title = {Complementarity in Categorical Quantum Mechanics},
Url = {http://dx.doi.org/10.1007/s10701-011-9585-9},
Volume = {42},
Year = {2012},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10701-011-9585-9}}
@book{montgomery:1980aa,
Author = {Susan Montgomery},
Date-Added = {2015-04-30 15:10:46 +0000},
Date-Modified = {2015-04-30 15:11:07 +0000},
Doi = {10.1007/BFb0091561},
Format-Detection = {telephone=no},
Keywords = {algebra, rings},
Msapplication-Tilecolor = {#FFFFFF},
Msapplication-Tileimage = {/static/0.9486/sites/link/images/ms-tileimage.png},
Publisher = {Springer},
Series = {Lecture Notes in Mathematics},
Title = {Fixed Rings of Finite Automorphism Groups of Associative Rings},
Viewport = {width=device-width, minimum-scale=1, maximum-scale=1},
Volume = {818},
Year = {1980},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/BFb0091561}}
@article{Kelly:2015aa,
Author = {Kelly, J. and Barends, R. and Fowler, A. G. and Megrant, A. and Jeffrey, E. and White, T. C. and Sank, D. and Mutus, J. Y. and Campbell, B. and Chen, Yu and Chen, Z. and Chiaro, B. and Dunsworth, A. and Hoi, I. -C. and Neill, C. and O/'Malley, P. J. J. and Quintana, C. and Roushan, P. and Vainsencher, A. and Wenner, J. and Cleland, A. N. and Martinis, John M.},
Date-Added = {2015-03-05 17:41:45 +0000},
Date-Modified = {2015-03-05 17:42:28 +0000},
Doi = {10.1038/nature14270},
Journal = {Nature},
Keywords = {quantum computing; error correcting codes;},
Month = {03},
Number = {7541},
Pages = {66--69},
Title = {State preservation by repetitive error detection in a superconducting quantum circuit},
Volume = {519},
Year = {2015},
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Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature14270}}
@inproceedings{qsharp,
title={Q\#: Enabling scalable quantum computing and development with a high-level domain-specific language},
author={Krysta M. Svore and Alan Geller and Matthias Troyer and John Azariah and Christopher Granade and Bettina Heim and Vadym Kliuchnikov and Mariia Mykhailova and Andres Paz and Martin Roetteler},
booktitle={Proceedings of the Real World Domain Specific Languages Workshop (RWDSL 2018)},
preprint={arXiv:1803.00652},
year=2018
}
@article{NW-2018,
author={Kang Feng Ng and Quanlong Wang},
title={Completeness of the {ZX}-calculus for Pure Qubit {Clifford}+{T} Quantum Mechanics},
Journal = {arXiv.org},
Number = {1801.07993},
year=2018
}
@article{NW-2017,
author={Kang Feng Ng and Quanlong Wang},
title = {A universal completion of the ZX-calculus},
year=2017,
preprint={arXiv:1706.09877}
}
@article{DKPdW-2019,
author={Ross Duncan and Aleks Kissinger and Simon Pedrix and John van de Wetering},
title={Graph-theoretic Simplification of Quantum Circuits with the {ZX}-calculus},
Journal = {arXiv.org},
Number = {1902.03178},
year=2019
}
@article{Raphael-Dias-da-Silva:2013aa,
Abstract = {One of the main goals in quantum circuit optimisation is to reduce the number of ancillary qubits and the depth of computation, to obtain robust computation. However, most of known techniques, based on local rewriting rules, for parallelising quantum circuits will require the addition of ancilla qubits, leading to an undesired space-time tradeoff. Recently several novel approaches based on measurement-based quantum computation (MBQC) techniques attempted to resolve this problem. The key element is to explore the global structure of a given circuit, defined via translation into a corresponding MBQC pattern. It is known that the parallel power of MBQC is superior to the quantum circuit model, and hence in these approaches one could apply the MBQC depth optimisation techniques to achieve a lower depth. However, currently, once the obtained parallel pattern is translated back to a quantum circuit, one should either increase the depth or add ancilla qubits. In this paper we characterise those computations where both optimisation could be achieved together. In doing so we present a new connection between two MBQC depth optimisation procedures, known as the maximally delayed generalised flow and signal shifting. This structural link will allow us to apply an MBQC qubit optimisation procedure known as compactification to a large class of pattern including all those obtained from any arbitrary quantum circuit. We also present a more efficient algorithm (compared to the existing one) for finding the maximally delayed generalised flow for graph states with flow.},
Author = {Raphael Dias da Silva, Einar Pius, Elham Kashefi},
Citation_Arxiv_Id = {1301.0351},
Citation_Author = {Kashefi, Elham},
Citation_Date = {2013/01/02},
Citation_Online_Date = {2013/01/02},
Citation_Pdf_Url = {http://arxiv.org/pdf/1301.0351},
Citation_Title = {Global Quantum Circuit Optimization},
Date-Added = {2015-01-16 00:18:44 +0000},
Date-Modified = {2015-01-16 00:18:44 +0000},
Eprint = {arXiv:1301.0351},
Journal = {arXiv:1301.0351},
Title = {Global Quantum Circuit Optimization},
Year = {2013},
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@incollection{Kashefi:2014vvv,
Author = {Markham, Damian and Kashefi, Elham},
Booktitle = {Horizons of the Mind. A Tribute to Prakash Panangaden},
Date-Added = {2015-01-16 00:13:43 +0000},
Date-Modified = {2015-01-16 00:14:02 +0000},
Doi = {10.1007/978-3-319-06880-0_22},
Editor = {van Breugel, Franck and Kashefi, Elham and Palamidessi, Catuscia and Rutten, Jan},
Isbn = {978-3-319-06879-4},
Pages = {427-453},
Publisher = {Springer International Publishing},
Series = {Lecture Notes in Computer Science},
Title = {Entanglement, Flow and Classical Simulatability in Measurement Based Quantum Computation},
Volume = {8464},
Year = {2014},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-319-06880-0_22}}
@article{larkin1987diagram,
Author = {Larkin, Jill H and Simon, Herbert A},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Journal = {Cognitive science},
Number = {1},
Pages = {65--100},
Publisher = {Wiley Online Library},
Title = {Why a diagram is (sometimes) worth ten thousand words},
Volume = {11},
Year = {1987}}
@inproceedings{Arrighi:2007aa,
Abstract = {One-dimensional quantum cellular automata (QCA) consist in a line of identical, finite dimensional quantum systems. These evolve in discrete time steps according to a local, shift-invariant unitary evolution. By local we mean that no instantaneous long-range communication can occur. In order to define these over a Hilbert space we must restrict to a base of finite, yet unbounded configurations. We show that QCA always admit a two-layered block representation, and hence the inverse QCA is again a QCA. This is a striking result since the property does not hold for classical one-dimensional cellular automata as defined over such finite configurations. As an example we discuss a bijective cellular automata which becomes non-local as a QCA, in a rare case of reversible computation which does not admit a straightforward quantization. We argue that a whole class of bijective cellular automata should no longer be considered to be reversible in a physical sense. Note that the same two-layered block representation result applies also over infinite configurations, as was previously shown for one-dimensional systems in the more elaborate formalism of operators algebras [9]. Here the proof is made simpler and self-contained, moreover we discuss a counterexample QCA in higher dimensions.},
Author = {Pablo Arrighi and Vincent Nesme and Reinhard Werner},
Booktitle = {2nd Int. Conf. on Language and Automata Theory and Applications, LATA 2008, Spain.},
Citation_Arxiv_Id = {0711.3517},
Citation_Author = {Werner, Reinhard},
Citation_Date = {2007/11/22},
Citation_Online_Date = {2007/11/22},
Citation_Pdf_Url = {http://arxiv.org/pdf/0711.3517},
Citation_Title = {One-dimensional quantum cellular automata over finite, unbounded configurations},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:0711.3517},
Keywords = {Quantum computation; cellular automata},
Series = {LNCS},
Title = {One-dimensional quantum cellular automata over finite, unbounded configurations},
Year = {2008},
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@book{rozenberg1999handbook,
Author = {Rozenberg, Grzegorz and Ehrig, Hartmut},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Publisher = {World scientific Singapore},
Title = {Handbook of graph grammars and computing by graph transformation},
Volume = {1},
Year = {1999}}
@article{Baez2014a,
Abstract = {Control theory uses "signal-flow diagrams" to describe processes where real-valued functions of time are added, multiplied by scalars, differentiated and integrated, duplicated and deleted. These diagrams can be seen as string diagrams for the symmetric monoidal category FinVect_k of finite-dimensional vector spaces over the field of rational functions k = R(s), where the variable s acts as differentiation and the monoidal structure is direct sum rather than the usual tensor product of vector spaces. For any field k we give a presentation of FinVect_k in terms of the generators used in signal flow diagrams. A broader class of signal-flow diagrams also includes "caps" and "cups" to model feedback. We show these diagrams can be seen as string diagrams for the symmetric monoidal category FinRel_k, where objects are still finite-dimensional vector spaces but the morphisms are linear relations. We also give a presentation for FinRel_k. The relations say, among other things, that the 1-dimensional vector space k has two special commutative dagger-Frobenius structures, such that the multiplication and unit of either one and the comultiplication and counit of the other fit together to form a bimonoid. This sort of structure, but with tensor product replacing direct sum, is familiar from the "ZX-calculus" obeyed by a finite-dimensional Hilbert space with two mutually unbiased bases.},
Author = {John C. Baez and Jason Erbele},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2016-09-29 11:20:10 +0000},
Eprint = {arXiv:1405.6881},
Journal = {Theory and Applications of Categories},
Number = {24},
Pages = {836-881},
Title = {Categories in Control},
Url = {http://www.tac.mta.ca/tac/volumes/30/24/30-24abs.html},
Volume = {30},
Year = {2015},
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@article{DBLP:journals/fuin/BruniMPT14,
Author = {Roberto Bruni and Ugo Montanari and Gordon D. Plotkin and Daniele Terreni},
Bibsource = {dblp computer science bibliography, http://dblp.org},
Biburl = {http://dblp.uni-trier.de/rec/bib/journals/fuin/BruniMPT14},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.3233/FI-2014-1103},
Journal = {Fundam. Inform.},
Number = {3-4},
Pages = {287--317},
Timestamp = {Mon, 24 Nov 2014 12:38:24 +0100},
Title = {On Hierarchical Graphs: Reconciling Bigraphs, Gs-monoidal Theories and Gs-graphs},
Url = {http://dx.doi.org/10.3233/FI-2014-1103},
Volume = {134},
Year = {2014},
Bdsk-Url-1 = {http://dx.doi.org/10.3233/FI-2014-1103}}
@article{selinger2013generators,
Author = {Selinger, Peter},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-10-29 18:08:38 +0000},
Doi = {10.2168/LMCS-11(2:10)2015},
Eprint = {arXiv:1310.6813},
Journal = {Logical Methods in Computer Science},
Number = {2:10},
Title = {Generators and relations for n-qubit Clifford operators},
Volume = {11},
Year = {2015},
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@incollection{Ghica2013,
Author = {Dan R. Ghica},
Booktitle = {Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Pages = {52--68},
Publisher = {Springer},
Timestamp = {26.11.14},
Title = {Diagrammatic Reasoning for Delay-Insensitive Asynchronous Circuits},
Year = {2013},
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@article{DBLP:journals/corr/BruniMMS13,
Author = {Roberto Bruni and Hern{\'{a}}n C. Melgratti and Ugo Montanari and Pawel Sobocinski},
Bibsource = {dblp computer science bibliography, http://dblp.org},
Biburl = {http://dblp.uni-trier.de/rec/bib/journals/corr/BruniMMS13},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.2168/LMCS-9(3:16)2013},
Journal = {Logical Methods in Computer Science},
Number = {3},
Timestamp = {Mon, 28 Oct 2013 16:56:55 +0100},
Title = {Connector algebras for {C/E} and {P/T} nets' interactions},
Url = {http://dx.doi.org/10.2168/LMCS-9(3:16)2013},
Volume = {9},
Year = {2013},
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@inproceedings{Bonchi2014b,
Author = {Filippo Bonchi and Pawe{\l} Soboci\'{n}ski and Fabio Zanasi},
Booktitle = {CONCUR`14},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Timestamp = {03.05.14},
Title = {A Categorical Semantics of Signal Flow Graphs},
Year = {2014}}
@inproceedings{Bonchi2015,
Author = {Filippo Bonchi and Pawe{\l} Soboci\'{n}ski and Fabio Zanasi},
Booktitle = {Principles of Programming Languages, {POPL} 15.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-10-20 14:39:27 +0000},
Doi = {10.1145/2676726.2676993},
Pages = {515--526},
Publisher = {{ACM}},
Timestamp = {26.11.14},
Title = {Full Abstraction for Signal Flow Graphs},
Year = {2015},
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@article{DBLP:journals/corr/abs-1304-3121,
Author = {Julian Rathke and Pawel Sobocinski and Owen Stephens},
Bibsource = {dblp computer science bibliography, http://dblp.org},
Biburl = {http://dblp.uni-trier.de/rec/bib/journals/corr/abs-1304-3121},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Journal = {CoRR},
Timestamp = {Thu, 02 May 2013 15:54:11 +0200},
Title = {Decomposing Petri nets},
Url = {http://arxiv.org/abs/1304.3121},
Volume = {abs/1304.3121},
Year = {2013},
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@inproceedings{DBLP:conf/apn/SobocinskiS14,
Author = {Pawel Sobocinski and Owen Stephens},
Booktitle = {Application and Theory of Petri Nets and Concurrency - 35th International Conference, {PETRI} {NETS} 2014, Tunis, Tunisia, June 23-27, 2014. Proceedings},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/978-3-319-07734-5_9},
Pages = {150--169},
Publisher = {Springer},
Series = {LNCS},
Title = {A Programming Language for Spatial Distribution of Net Systems},
Volume = {8489},
Year = {2014},
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@inproceedings{DBLP:conf/calco/SobocinskiS13,
Author = {Pawel Sobocinski and Owen Stephens},
Booktitle = {Algebra and Coalgebra in Computer Science - 5th International Conference, {CALCO} 2013, Warsaw, Poland, September 3-6, 2013. Proceedings},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/978-3-642-40206-7_29},
Pages = {346--352},
Publisher = {Springer},
Series = {LNCS},
Title = {Penrose: Putting Compositionality to Work for Petri Net Reachability},
Volume = {8089},
Year = {2013},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-40206-7_29}}
@inproceedings{DBLP:conf/rp/RathkeSS14,
Author = {Julian Rathke and Pawel Sobocinski and Owen Stephens},
Booktitle = {Reachability Problems - 8th International Workshop, {RP} 2014, Oxford, UK, September 22-24, 2014. Proceedings},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/978-3-319-11439-2_18},
Pages = {230--243},
Publisher = {Springer},
Series = {LNCS},
Title = {Compositional Reachability in Petri Nets},
Volume = {8762},
Year = {2014},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-319-11439-2_18}}
@article{johansson2011conjecture,
Author = {Johansson, Moa and Dixon, Lucas and Bundy, Alan},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Journal = {Journal of Automated Reasoning},
Number = {3},
Pages = {251--289},
Publisher = {Springer},
Title = {Conjecture synthesis for inductive theories},
Volume = {47},
Year = {2011}}
@article{PhysRevLett.94.060503,
Author = {Plenio, M. B. and Eisert, J. and Drei\ss{}ig, J. and Cramer, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevLett.94.060503},
Issue = {6},
Journal = {Phys. Rev. Lett.},
Month = {Feb},
Numpages = {4},
Pages = {060503},
Title = {Entropy, Entanglement, and Area: Analytical Results for Harmonic Lattice Systems},
Volume = {94},
Year = {2005},
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Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.94.060503}}
@article{1367-2630-9-10-361,
Abstract = {In a recent article Anders et al 2006 Phys. Rev. Lett. 97 107206, we have presented a class of states which is suitable as a variational set to find ground states in spin systems of arbitrary spatial dimension and with long-range entanglement. Here, we continue the exposition of our technique, extend from spin 1/2 to higher spins and use the boson Hubbard model as a non-trivial example to demonstrate our scheme.},
Author = {Simon Anders and Hans J Briegel and Wolfgang D{\"u}r},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1088/1367-2630/9/10/361},
Journal = {New Journal of Physics},
Number = {10},
Pages = {361},
Title = {A variational method based on weighted graph states},
Volume = {9},
Year = {2007},
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Bdsk-Url-1 = {http://stacks.iop.org/1367-2630/9/i=10/a=361},
Bdsk-Url-2 = {http://dx.doi.org/10.1088/1367-2630/9/10/361}}
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Title = {Department of {H}ealth: The National Programme for {IT} in the {NHS}},
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@inproceedings{harrison-sfm,
Address = {Bertinoro, Italy},
Author = {John Harrison},
Booktitle = {Formal Methods for Hardware Verification, 6th International School on Formal Methods for the Design of Computer, Communication, and Software Systems, SFM 2006},
Date = {May 2006},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Editor = {Marco Bernardo and Alessandro Cimatti},
Pages = {211--242},
Publisher = {Springer-Verlag},
Series = {Lecture Notes in Computer Science},
Title = {Floating-Point Verification using Theorem Proving},
Volume = 3965,
Year = 2006,
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@article{Dowson:1997:ASF:251880.251992,
Author = {Dowson, Mark},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1145/251880.251992},
Journal = {SIGSOFT Softw. Eng. Notes},
Month = mar,
Number = {2},
Publisher = {ACM},
Title = {The {A}riane 5 Software Failure},
Volume = {22},
Year = {1997},
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@article{Nuseibeh:2002aa,
Author = {Nuseibeh, B.},
Citation_Abstract_Html_Url = {http://ieeexplore.ieee.org/articleDetails.jsp?arnumber=589224},
Citation_Author = {Nuseibeh, B.},
Citation_Date = {May-June 1997},
Citation_Doi = {10.1109/MS.1997.589224},
Citation_Firstpage = {15},
Citation_Issn = {0740-7459},
Citation_Issue = {3},
Citation_Journal_Title = {Software, IEEE},
Citation_Keywords = {Accidents; Control systems; Educational institutions; Failure analysis; Hardware; Project management; Risk management; Software safety; Testing; Transportation;},
Citation_Language = {English},
Citation_Lastpage = {16},
Citation_Pdf_Url = {http://ieeexplore.ieee.org/iel4/52/12938/00589224.pdf?arnumber=589224},
Citation_Publisher = {IEEE},
Citation_Title = {Ariane 5: Who Dunnit?},
Citation_Volume = {14},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Description = {IEEE Xplore. Delivering full text access to the world's highest quality technical literature in engineering and technology.},
Doi = {10.1109/MS.1997.589224},
Journal = {Software, IEEE},
Number = {3},
Pages = {15 - 16},
Title = {Ariane 5: Who Dunnit?},
Volume = {14},
Year = {2002},
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@techreport{Allen:2010aa,
Author = {R. Allen},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Institution = {CSE , CSE-HEC , STFC},
Number = {DL-TR-2010-008},
Title = {Computing Grand Challenges},
Url = {http://purl.org/net/epubs/work/50400},
Year = {2010},
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@article{Kissinger:2014ac,
Annote = {Multigraph categories are symmetric monoidal categories where each object is equipped with a special commutative Frobenius algebra (SCFA). Dagger-multigraph categories are the same, but with dagger-symmetric monoidal categories and dagger-SCFAs. In this paper, we show that finite matrices over a field K of characteristic 0 are complete for multigraph categories, and that finite matrices where K has a non-trivial involution are complete for dagger-multigraph categories.},
Author = {Aleks Kissinger},
Citation_Arxiv_Id = {1406.5942},
Citation_Author = {Kissinger, Aleks},
Citation_Date = {2014/06/23},
Citation_Online_Date = {2014/06/23},
Citation_Pdf_Url = {http://arxiv.org/pdf/1406.5942},
Citation_Title = {Finite matrices are complete for (dagger-)multigraph categories},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1406.5942},
Journal = {arXiv preprint},
Keywords = {graphical calculi; algebra; category theory; categorical quantum mechanics},
Title = {Finite matrices are complete for (dagger-)multigraph categories},
Year = {2014},
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@article{gonthier2008formal,
Author = {Gonthier, Georges},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Journal = {Notices of the AMS},
Number = {11},
Pages = {1382--1393},
Title = {Formal proof--the four-color theorem},
Volume = {55},
Year = {2008},
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@phdthesis{Gurski:2006aa,
Author = {Nick Gurski},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Keywords = {category theory; higher categories},
School = {University of Chicago},
Title = {An algebraic theory of tricategories},
Year = {2006},
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@article{Shulman:2010aa,
Abstract = {We present a method of constructing symmetric monoidal bicategories from symmetric monoidal double categories that satisfy a lifting condition. Such symmetric monoidal double categories frequently occur in nature, so the method is widely applicable, though not universally so.},
Author = {Michael A. Shulman},
Citation_Arxiv_Id = {1004.0993},
Citation_Author = {Shulman, Michael A.},
Citation_Date = {2010/04/07},
Citation_Online_Date = {2010/04/07},
Citation_Pdf_Url = {http://arxiv.org/pdf/1004.0993},
Citation_Title = {Constructing symmetric monoidal bicategories},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1004.0993},
Title = {Constructing symmetric monoidal bicategories},
Year = {2010},
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@misc{Hackney:2012ab,
Abstract = {The category of (colored) props is an enhancement of the category of colored operads, and thus of the category of small categories. In this paper, the second in a series on "higher props," we show that the category of all small colored simplicial props admits a cofibrantly generated model category structure. With this model structure, the forgetful functor from props to operads is a right Quillen functor.},
Author = {Philip Hackney and Marcy Robertson},
Citation_Arxiv_Id = {1209.1087},
Citation_Author = {Robertson, Marcy},
Citation_Date = {2012/09/05},
Citation_Online_Date = {2012/09/05},
Citation_Pdf_Url = {http://arxiv.org/pdf/1209.1087},
Citation_Title = {The homotopy theory of simplicial props},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1209.1087},
Howpublished = {arXiv.org},
Keywords = {category theory; higher categories; PROPs; homotopy theory},
Title = {The homotopy theory of simplicial props},
Year = {2012},
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@misc{Hackney:2012aa,
Abstract = {The category of (colored) props is an enhancement of the category of colored operads, and thus of the category of small categories. The titular category has nice formal properties: it is bicomplete and is a symmetric monoidal category, with monoidal product closely related to the Boardman-Vogt tensor product of operads. Tools developed in this article, which is the first part of a larger work, include a generalized version of multilinearity of functors, a free prop construction defined on certain "generalized graphs", and the relationship between the category of props and the categories of permutative categories and of operads.},
Author = {Philip Hackney and Marcy Robertson},
Citation_Arxiv_Id = {1207.2773},
Citation_Author = {Robertson, Marcy},
Citation_Date = {2012/07/11},
Citation_Online_Date = {2014/01/28},
Citation_Pdf_Url = {http://arxiv.org/pdf/1207.2773},
Citation_Title = {On the category of props},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1207.2773},
Howpublished = {arXiv.org},
Keywords = {category theory; higher categories; PROPs},
Title = {On the category of props},
Year = {2012},
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@misc{Aharonov:2014aa,
Abstract = {The pigeonhole principle: "If you put three pigeons in two pigeonholes at least two of the pigeons end up in the same hole" is an obvious yet fundamental principle of Nature as it captures the very essence of counting. Here however we show that in quantum mechanics this is not true! We find instances when three quantum particles are put in two boxes, yet no two particles are in the same box. Furthermore, we show that the above "quantum pigeonhole principle" is only one of a host of related quantum effects, and points to a very interesting structure of quantum mechanics that was hitherto unnoticed. Our results shed new light on the very notions of separability and correlations in quantum mechanics and on the nature of interactions. It also presents a new role for entanglement, complementary to the usual one. Finally, interferometric experiments that illustrate our effects are proposed.},
Author = {Y. Aharonov and F. Colombo and S. Popescu and I. Sabadini and D.C.Struppa and J. Tollaksen},
Citation_Arxiv_Id = {1407.3194},
Citation_Author = {Tollaksen, J.},
Citation_Date = {2014/07/11},
Citation_Online_Date = {2014/07/11},
Citation_Pdf_Url = {http://arxiv.org/pdf/1407.3194},
Citation_Title = {The quantum pigeonhole principle and the nature of quantum correlations},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1407.3194},
Howpublished = {arXiv},
Keywords = {quantum theory},
Title = {The quantum pigeonhole principle and the nature of quantum correlations},
Year = {2014},
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@article{Baez1997125,
Abstract = {A 2-Hilbert space is a category with structures and properties analogous to those of a Hilbert space. More precisely, we define a 2-Hilbert space to be an Abelian category enriched over Hilb with a ∗-structure, conjugate-linear on the hom-sets, satisfying ⦠fg, h⦔=⦠g, f*h⦔=⦠f, hg*⦔. We also define monoidal, braided monoidal, and symmetric monoidal versions of 2-Hilbert spaces, which we call 2-H*-algbebras, braided 2-H*-algebras, and symmetric 2-H*-algbebras, and we describe the relation between these and tangles in two, three, and four dimensions, respectively. We prove a generalized Doplicher--Roberts theorem starting that every symmetric 2-H*-algebra is equivalent to the category Rep(G) of continuous unitary finite-dimensional representations of some compact supergroupoidG. The equivalence is given by a categorified version of the Gelfand transform; we also construct a categorified version of the Fourier transform whenGis a compact Abelian group. Finally, we characterize Rep(G) by its universal properties whenGis a compact classical group. For example, Rep(U(n)) is the free connected symmetric 2-H*-algebra on one even object of dimensionn. },
Author = {John C. Baez},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1006/aima.1997.1617},
Issn = {0001-8708},
Journal = {Advances in Mathematics},
Number = {2},
Pages = {125 - 189},
Title = {Higher-Dimensional Algebra II. 2-Hilbert Spaces},
Volume = {127},
Year = {1997},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0001870897916170},
Bdsk-Url-2 = {http://dx.doi.org/10.1006/aima.1997.1617}}
@misc{Leinster:1998aa,
Abstract = {A concise guide to very basic bicategory theory, from the definition of a bicategory to the coherence theorem},
Author = {Tom Leinster},
Citation_Arxiv_Id = {math/9810017},
Citation_Author = {Leinster, Tom},
Citation_Date = {1998/10/04},
Citation_Online_Date = {1998/10/04},
Citation_Pdf_Url = {http://arxiv.org/pdf/math/9810017},
Citation_Title = {Basic Bicategories},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arxiv:math/9810017},
Keywords = {higher categories; category theory},
Title = {Basic Bicategories},
Year = {1998},
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@incollection{Baez:1997:ctcs:intro,
Author = {Baez, JohnC.},
Booktitle = {Category Theory and Computer Science},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/BFb0026978},
Editor = {Moggi, Eugenio and Rosolini, Giuseppe},
Isbn = {978-3-540-63455-3},
Language = {English},
Pages = {1-33},
Publisher = {Springer Berlin Heidelberg},
Series = {Lecture Notes in Computer Science},
Title = {An introduction to n-categories},
Volume = {1290},
Year = {1997},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/BFb0026978}}
@article{Baez1996196,
Abstract = {We begin with a brief sketch of what is known and conjectured concerning braided monoidal 2-categories and their relevance to 4d \{TQFTs\} and 2-tangles. Then we give concise definitions of semistrict monoidal 2-categories and braided monoidal 2-categories and show how these may be unpacked to give long explicit definitions similar to, but not quite the same as, those given by previously Kapranov and Voevodsky. Finally, we describe how to construct a semistrict braided monoidal 2-category Z(C) as the ``center'' of a semistrict monoidal category C, in a manner analogous to the construction of a braided monoidal category as the center of a monoidal category. As a corollary this yields a strictification theorem for braided monoidal 2-categories. },
Author = {John C Baez and Martin Neuchl},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {http://dx.doi.org/10.1006/aima.1996.0052},
Eprint = {arXiv:q-alg/9511013},
Issn = {0001-8708},
Journal = {Advances in Mathematics},
Number = {2},
Pages = {196 - 244},
Title = {Higher Dimensional Algebra: I. Braided Monoidal 2-Categories},
Url = {http://www.sciencedirect.com/science/article/pii/S0001870896900523},
Volume = {121},
Year = {1996},
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Bdsk-Url-2 = {http://dx.doi.org/10.1006/aima.1996.0052}}
@inproceedings{DBLP:conf/lics/Vicary13,
Author = {Jamie Vicary},
Bibsource = {DBLP, http://dblp.uni-trier.de},
Booktitle = {LICS},
Crossref = {DBLP:conf/lics/2013},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1109/LICS.2013.14},
Eprint = {arxiv:1209.3917},
Keywords = {categorical quantum mechanics; higher categories; graphical calculi; quantum computing},
Pages = {93-102},
Title = {Topological Structure of Quantum Algorithms},
Year = {2013},
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Bdsk-Url-1 = {http://dx.doi.org/10.1109/LICS.2013.14}}
@proceedings{DBLP:conf/lics/2013,
Bibsource = {DBLP, http://dblp.uni-trier.de},
Booktitle = {LICS},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Ee = {http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6570844},
Isbn = {978-1-4799-0413-6},
Publisher = {IEEE Computer Society},
Title = {28th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2013, New Orleans, LA, USA, June 25-28, 2013},
Year = {2013}}
@article{DBLP:journals/entcs/StayV13,
Author = {Mike Stay and Jamie Vicary},
Bibsource = {DBLP, http://dblp.uni-trier.de},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1016/j.entcs.2013.09.022},
Eprint = {arXiv:1301.3393},
Journal = {Electr. Notes Theor. Comput. Sci.},
Keywords = {higher categories;},
Pages = {367-382},
Title = {Bicategorical Semantics for Nondeterministic Computation},
Volume = {298},
Year = {2013},
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Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.entcs.2013.09.022}}
@misc{Vicary:2012aa,
Abstract = {We propose a 2-categorical formalism for describing classical information, quantum systems, and their interactions, based on the principle that classical information can be encoded as correlations between quantum systems. Applying this in the 2-category of 2-Hilbert spaces recovers ordinary quantum theory. The formalism gives a simple, graphical way to describe the specification and implementation of certain quantum procedures, which we use to investigate quantum teleportation, dense coding, complementarity and quantum erasure, verifying our results computationally using a software package.},
Author = {Jamie Vicary},
Citation_Arxiv_Id = {1207.4563},
Citation_Author = {Vicary, Jamie},
Citation_Date = {2012/07/19},
Citation_Online_Date = {2012/07/19},
Citation_Pdf_Url = {http://arxiv.org/pdf/1207.4563},
Citation_Title = {Higher Quantum Theory},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1207.4563},
Keywords = {categorical quantum mechanics; higher categories; quantum computing},
Title = {Higher Quantum Theory},
Year = {2012},
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@inproceedings{DBLP:conf/lics/Vicary12,
Author = {Jamie Vicary},
Bibsource = {DBLP, http://dblp.uni-trier.de},
Booktitle = {LICS},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1109/LICS.2012.70},
Pages = {606-615},
Title = {Higher Semantics of Quantum Protocols},
Year = {2012},
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Bdsk-Url-1 = {http://dx.doi.org/10.1109/LICS.2012.70}}
@article{PhysRevLett.82.1060,
Author = {Brennen, Gavin K. and Caves, Carlton M. and Jessen, Poul S. and Deutsch, Ivan H.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevLett.82.1060},
Issue = {5},
Journal = {Phys. Rev. Lett.},
Month = {Feb},
Numpages = {0},
Pages = {1060--1063},
Publisher = {American Physical Society},
Title = {Quantum Logic Gates in Optical Lattices},
Url = {http://link.aps.org/doi/10.1103/PhysRevLett.82.1060},
Volume = {82},
Year = {1999},
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@article{10.1109/SWAT.1974.13,
Address = {Los Alamitos, CA, USA},
Author = {J. A. Goguen and J. W. Thatcher},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {http://doi.ieeecomputersociety.org/10.1109/SWAT.1974.13},
Issn = {0272-5428},
Journal = {2013 IEEE 54th Annual Symposium on Foundations of Computer Science},
Pages = {63-77},
Publisher = {IEEE Computer Society},
Title = {Initial algebra semantics},
Volume = {0},
Year = {1974},
Bdsk-Url-1 = {http://doi.ieeecomputersociety.org/10.1109/SWAT.1974.13}}
@book{Blackburn:2001:ML:381193,
Address = {New York, NY, USA},
Author = {Blackburn, Patrick and de Rijke, Maarten and Venema, Yde},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Isbn = {0-521-80200-8},
Publisher = {Cambridge University Press},
Title = {Modal Logic},
Year = {2001}}
@incollection{Ghamarian:2012aa,
Author = {Ghamarian, AmirHossein and Rensink, Arend},
Booktitle = {Graph Transformations},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/978-3-642-33654-6_16},
Editor = {Ehrig, Hartmut and Engels, Gregor and Kreowski, Hans-J{\"o}rg and Rozenberg, Grzegorz},
Isbn = {978-3-642-33653-9},
Pages = {234-248},
Publisher = {Springer Berlin Heidelberg},
Series = {Lecture Notes in Computer Science},
Title = {Generalised Compositionality in Graph Transformation},
Url = {http://dx.doi.org/10.1007/978-3-642-33654-6_16},
Volume = {7562},
Year = {2012},
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@incollection{Rensink:2012aa,
Author = {Rensink, Arend and Zambon, Eduardo},
Booktitle = {Graph Transformations},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/978-3-642-33654-6_5},
Editor = {Ehrig, Hartmut and Engels, Gregor and Kreowski, Hans-J{\"o}rg and Rozenberg, Grzegorz},
Isbn = {978-3-642-33653-9},
Pages = {66-80},
Publisher = {Springer Berlin Heidelberg},
Series = {Lecture Notes in Computer Science},
Title = {Pattern-Based Graph Abstraction},
Url = {http://dx.doi.org/10.1007/978-3-642-33654-6_5},
Volume = {7562},
Year = {2012},
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@book{BN98,
Address = {Cambridge},
Author = {F. Baader and T. Nipkow},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Publisher = {Cambridge University Press},
Title = {Term Rewriting and All That},
Year = 1998}
@article{RevModPhys.84.621,
Author = {Weedbrook, Christian and Pirandola, Stefano and Garc\'ia-Patr\'on, Ra\'ul and Cerf, Nicolas J. and Ralph, Timothy C. and Shapiro, Jeffrey H. and Lloyd, Seth},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/RevModPhys.84.621},
Issue = {2},
Journal = {Rev. Mod. Phys.},
Month = {May},
Numpages = {0},
Pages = {621--669},
Publisher = {American Physical Society},
Title = {Gaussian quantum information},
Url = {http://link.aps.org/doi/10.1103/RevModPhys.84.621},
Volume = {84},
Year = {2012},
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@article{Moggi:1991:NCM:116981.116984,
Acmid = {116984},
Address = {Duluth, MN, USA},
Author = {Moggi, Eugenio},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1016/0890-5401(91)90052-4},
Issn = {0890-5401},
Issue_Date = {July 1991},
Journal = {Inf. Comput.},
Month = jul,
Number = {1},
Numpages = {38},
Pages = {55--92},
Publisher = {Academic Press, Inc.},
Title = {Notions of Computation and Monads},
Url = {http://dx.doi.org/10.1016/0890-5401(91)90052-4},
Volume = {93},
Year = {1991},
Bdsk-Url-1 = {http://dx.doi.org/10.1016/0890-5401(91)90052-4}}
@article{PhysRevA.87.032332,
Author = {Giles, Brett and Selinger, Peter},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevA.87.032332},
Issue = {3},
Journal = {Phys. Rev. A},
Month = {Mar},
Numpages = {7},
Pages = {032332},
Publisher = {American Physical Society},
Title = {Exact synthesis of multiqubit Clifford+$T$ circuits},
Url = {http://link.aps.org/doi/10.1103/PhysRevA.87.032332},
Volume = {87},
Year = {2013},
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Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevA.87.032332}}
@mastersthesis{Schroder:2013aa,
Author = {Christian A. Schr{\"o}der},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
School = {University of Oxford},
Title = {The ZX calculus is incomplete for non-stabilizer quantum mechanics},
Year = {2013},
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@incollection{Gay:2008aa,
Author = {Gay, Simon J. and Nagarajan, Rajagopal and Papanikolaou, Nikolaos},
Booktitle = {Computer Aided Verification},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/978-3-540-70545-1_51},
Editor = {Gupta, Aarti and Malik, Sharad},
Isbn = {978-3-540-70543-7},
Pages = {543-547},
Publisher = {Springer Berlin Heidelberg},
Series = {Lecture Notes in Computer Science},
Title = {QMC: A Model Checker for Quantum Systems},
Url = {http://dx.doi.org/10.1007/978-3-540-70545-1_51},
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@article{Davidson:2012aa,
Author = {T. Davidson and S. J. Gay and H. Mlnarik and R. Nagarajan and N. Papanikolaou},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Journal = {International Journal of Unconventional Computing},
Number = {1},
Pages = {73-98},
Title = {Model Checking for Communicating Quantum Processes},
Volume = {8},
Year = {2012}}
@article{Michael-J.-Bremner1:2011aa,
Abstract = {We consider quantum computations comprising only commuting gates, known as IQP computations, and provide compelling evidence that the task of sampling their output probability distributions is unlikely to be achievable by any efficient classical means. More specifically, we introduce the class post-IQP of languages decided with bounded error by uniform families of IQP circuits with post-selection, and prove first that post-IQP equals the classical class PP. Using this result we show that if the output distributions of uniform IQP circuit families could be classically efficiently sampled, either exactly in total variation distance or even approximately up to 41 per cent multiplicative error in the probabilities, then the infinite tower of classical complexity classes known as the polynomial hierarchy would collapse to its third level. We mention some further results on the classical simulation properties of IQP circuit families, in particular showing that if the output distribution results from measurements on only lines then it may, in fact, be classically efficiently sampled.},
Author = {Michael J. Bremner and Richard Jozsa and Dan J. Shepherd},
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Citation_Author_Email = {michael.bremner@itp.uni-hannover.de},
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Citation_Section = {Research articles},
Citation_Title = {Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy},
Citation_Volume = {467},
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Dc.Title = {Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy},
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Eprint = {arXiv:1005.1407},
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@inproceedings{Aaronson:2011:CCL:1993636.1993682,
Acmid = {1993682},
Address = {New York, NY, USA},
Author = {Aaronson, Scott and Arkhipov, Alex},
Booktitle = {Proceedings of the Forty-third Annual ACM Symposium on Theory of Computing},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1145/1993636.1993682},
Eprint = {arXiv:1011.3245},
Isbn = {978-1-4503-0691-1},
Keywords = {\#p, BGP, bosons, linear optics, permanent, polynomial hierarchy, random self-reducibility, sampling},
Location = {San Jose, California, USA},
Numpages = {10},
Pages = {333--342},
Publisher = {ACM},
Series = {STOC '11},
Title = {The Computational Complexity of Linear Optics},
Url = {http://doi.acm.org/10.1145/1993636.1993682},
Year = {2011},
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@inproceedings{Boneh:1995aa,
Author = {D. Boneh and R. J. Lipton},
Booktitle = {Advances in Cryptology - CRYPTO '95},
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Doi = {10.1007/3-540-44750-4_34},
Editor = {Don Coppersmith},
Pages = {424-437},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {Quantum cryptoanalysis of hidden linear functions},
Volume = {963},
Year = {1995},
Bdsk-Url-1 = {http://dx.doi.org/10.1007/3-540-44750-4_34}}
@misc{Jordan:quant-algo-zoo,
Author = {Stephen Jordan},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Description = {A comprehensive list of quantum algorithms.},
Howpublished = {http://math.nist.gov/quantum/zoo/},
Keywords = {quantum computing; algorithms},
Title = {Quantum Algorithm Zoo},
Url = {http://math.nist.gov/quantum/zoo/},
Bdsk-Url-1 = {http://math.nist.gov/quantum/zoo/}}
@inproceedings{Simon:1994aa,
Author = {D. Simon},
Booktitle = {Proceedings of the 35th Symposium on Foundations of Computer Science},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Pages = {116-123},
Title = {On the Power of Quantum Computation},
Year = {1994}}
@article{Lloyd:1996aa,
Abstract = {Feynman's 1982 conjecture, that quantum computers can be programmed to simulate any local quantum system, is shown to be correct},
Author = {Seth Lloyd},
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Citation_Date = {08/23/1996},
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Citation_Title = {Universal Quantum Simulators},
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@article{Pusey:2012aa,
Annote = {10.1038/nphys2309},
Author = {Pusey, Matthew F. and Barrett, Jonathan and Rudolph, Terry},
Date = {2012/06//print},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Isbn = {1745-2473},
Journal = {Nat Phys},
Keywords = {quantum theory},
L3 = {http://www.nature.com/nphys/journal/v8/n6/abs/nphys2309.html#supplementary-information},
M3 = {10.1038/nphys2309},
Month = {06},
Number = {6},
Pages = {475--478},
Publisher = {Nature Publishing Group},
Title = {On the reality of the quantum state},
Ty = {JOUR},
Url = {http://dx.doi.org/10.1038/nphys2309},
Volume = {8},
Year = {2012},
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@inproceedings{Bove:2009aa,
Author = {Ana Bove and Peter Dybjer and Ulf Norell},
Booktitle = {proceedings of TPHOLs},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Publisher = {Springer},
Title = {A Brief Overview of Agda -- A Functional Language with Dependent Types},
Year = {2009},
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@inproceedings{Ardeshir-Larijani:2013aa,
Author = {E. Ardeshir-Larijani and S. J. Gay and R. Nagarajan},
Booktitle = {Proceedings of the 19th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS)},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Pages = {466-480},
Publisher = {Springer},
Series = {LNCS},
Title = {Equivalence Checking of Quantum Protocols},
Volume = {7795},
Year = {2013},
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@article{Weitenberg:2011aa,
Abstract = {We present a complete architecture for scalable quantum computation with ultracold atoms in optical lattices using optical tweezers focused to the size of a lattice spacing. We discuss three different two-qubit gates based on local collisional interactions. The gates between arbitrary qubits require the transport of atoms to neighboring sites. We numerically optimize the nonadiabatic transport of the atoms through the lattice and the intensity ramps of the optical tweezer in order to maximize the gate fidelities. We find overall gate times of a few 100μ<math><mrow><mn>100</mn><mspace width="0.28em"></mspace><mi>μ</mi></mrow></math>s, while keeping the error probability due to vibrational excitations and spontaneous scattering below 10−3<math><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>. The requirements on the positioning error and intensity noise of the optical tweezer and the magnetic field stability are analyzed and we show that atoms in optical lattices could meet the requirements for fault-tolerant scalable quantum computing.},
Author = {Christof Weitenberg and Stefan Kuhr and Klaus M{\o}lmer and Jacob F. Sherson},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevA.84.032322},
Journal = {Phys. Rev. A},
Number = {032322},
Title = {Quantum computation architecture using optical tweezers},
Viewport = {width=device-width},
Volume = {84},
Year = {2011},
Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.84.032322}}
@article{Endres:2013aa,
Abstract = {Correlation functions play an important role for the theoretical and experimental characterization of many-body systems. In solid-state systems, they are usually determined through scattering experiments, whereas in cold gases systems, time-of-flight, and in situ absorption imaging are the standard observation techniques. However, none of these methods allow the in situ detection of spatially resolved correlation functions at the single-particle level. Here, we give a more detailed account of recent advances in the detection of correlation functions using in situ fluorescence imaging of ultracold bosonic atoms in an optical lattice. This method yields single-site- and single-atom-resolved images of the lattice gas in a single experimental run, thus gaining direct access to fluctuations in the many-body system. As a consequence, the detection of correlation functions between an arbitrary set of lattice sites is possible. This enables not only the detection of two-site correlation functions but also the evaluation of non-local correlations, which originate from an extended region of the system and are used for the characterization of quantum phases that do not possess (quasi-)long-range order in the traditional sense.},
Author = {M. Endres and M. Cheneau and T. Fukuhara and C. Weitenberg and P. Schau{\ss} and C. Gross and L. Mazza and M. C. Ba{\~n}uls and L. Pollet and I. Bloch and S. Kuhr},
Citation_Abstract_Html_Url = {http://link.springer.com/article/10.1007/s00340-013-5552-9},
Citation_Author = {S. Kuhr},
Citation_Author_Email = {manuel.endres@mpq.mpg.de},
Citation_Author_Institution = {University of Strathclyde},
Citation_Doi = {10.1007/s00340-013-5552-9},
Citation_Firstpage = {27},
Citation_Fulltext_Html_Url = {http://link.springer.com/article/10.1007/s00340-013-5552-9/fulltext.html},
Citation_Issn = {1432-0649},
Citation_Issue = {1},
Citation_Journal_Abbrev = {Appl. Phys. B},
Citation_Journal_Title = {Applied Physics B},
Citation_Language = {en},
Citation_Lastpage = {39},
Citation_Online_Date = {2013/08/02},
Citation_Pdf_Url = {http://link.springer.com/content/pdf/10.1007%2Fs00340-013-5552-9.pdf},
Citation_Publication_Date = {2013/10/01},
Citation_Publisher = {Springer Berlin Heidelberg},
Citation_Springer_Api_Url = {http://api.springer.com/metadata/pam?q=doi:10.1007/s00340-013-5552-9&api_key=},
Citation_Title = {Single-site- and single-atom-resolved measurement of correlation functions},
Citation_Volume = {113},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/s00340-013-5552-9},
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Journal = {Applied Physics B},
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Number = {1},
Pages = {27-39},
Title = {Single-site- and single-atom-resolved measurement of correlation functions},
Viewport = {width=device-width, minimum-scale=1, maximum-scale=1},
Volume = {113},
Year = {2013},
Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00340-013-5552-9}}
@inproceedings{Jacobs:2011ab,
Abstract = {The paper investigates non-deterministic, probabilistic and quantum walks, from the perspective of coalgebras and monads. Non-deterministic and probabilistic walks are coalgebras of a monad (powerset and distribution), in an obvious manner. It is shown that also quantum walks are coalgebras of a new monad, involving additional control structure. This new monad is also used to describe Turing machines coalgebraically, namely as controlled `walks' on a tape},
Author = {Bart Jacobs},
Booktitle = {Foundations of Software Science and Computational Structures (FOSSACS 2011)},
Citation_Abstract_Html_Url = {http://link.springer.com/chapter/10.1007/978-3-642-19805-2_2},
Citation_Author = {Bart Jacobs},
Citation_Author_Institution = {Radboud University Nijmegen},
Citation_Doi = {10.1007/978-3-642-19805-2_2},
Citation_Firstpage = {12},
Citation_Inbook_Title = {Foundations of Software Science and Computational Structures},
Citation_Isbn = {978-3-642-19805-2},
Citation_Lastpage = {26},
Citation_Pdf_Url = {http://link.springer.com/content/pdf/10.1007%2F978-3-642-19805-2_2.pdf},
Citation_Publication_Date = {2011/01/01},
Citation_Publisher = {Springer Berlin Heidelberg},
Citation_Springer_Api_Url = {http://api.springer.com/metadata/pam?q=doi:10.1007/978-3-642-19805-2_2&api_key=},
Citation_Title = {Coalgebraic Walks, in Quantum and Turing Computation},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/978-3-642-19805-2_2},
Format-Detection = {telephone=no},
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Pages = {12-26},
Series = {Lecture Notes in Computer Science},
Title = {Coalgebraic Walks, in Quantum and Turing Computation},
Viewport = {width=device-width, minimum-scale=1, maximum-scale=1},
Volume = {6604},
Year = {2011},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-19805-2_2}}
@article{schreiber2011differential,
Author = {Schreiber, Urs},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Journal = {Habilitation, Hamburg},
Title = {Differential cohomology in a cohesive∞-topos},
Year = {2011},
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@article{schreiber2012quantum,
Author = {Schreiber, Urs and Shulman, Michael},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Journal = {Quantum Physics and Logic},
Pages = {240},
Title = {Quantum gauge field theory in cohesive homotopy type theory},
Year = {2012},
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@inproceedings{Jacobs:2013aa,
Author = {B. Jacobs},
Booktitle = {Mathematical Foundations of Program Semantics (MFPS 2013)},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-10-10 07:55:09 +0000},
Doi = {10.1016/j.entcs.2013.09.016},
Editor = {D. Kozen and M. Mislove},
Pages = {233-255},
Series = {ENTCS},
Title = {On Block Structures in Quantum Computation},
Volume = {298},
Year = {2013},
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@article{Jacobs:2012aa,
Abstract = {Traditionally in categorical logic predicates on an object/type X are represented as subobjects of X. Here we break with that tradition and use maps of the form p : X --> X + X with [id, id] o p = id as predicates. This new view gives a more dynamic, measurement-oriented view on predicates, that works well especially in a quantitative setting. In classical logic (in the category of sets) these new predicates coincide with the traditional ones (subsets, or characteristic maps X --> {0,1}); in probabilistic logic (in the category of sets and stochastic matrices), the new predicates correspond to fuzzy predicates X --> [0,1]; and in quantum logic (in Hilbert spaces) they correspond to effects (positive endomaps below the identity), which may be understood as fuzzy predicates on a changed basis. It is shown that, under certain conditions about coproducts +, predicates p : X --> X + X form effect algebras and carry a scalar multiplication (with probabilities). Suitable substitution functors give rise to indexed/fibred categories. In the quantum case the famous Born rule - describing the probability of observation outcomes - follows directly from the form of these substitution functors: probability calculation becomes substitution in predicate logic. Moreover, the characteristic maps associated with predicates provide tests in a dynamic logic, and turn out to capture measurement in a form that uniformly covers the classical, probabilistic and quantum case. The probabilities incorporated in predicates (as eigenvalues) serves as weights for the possible measurement outcomes.},
Author = {Bart Jacobs},
Citation_Arxiv_Id = {1205.3940},
Citation_Author = {Jacobs, Bart},
Citation_Date = {2012/05/17},
Citation_Online_Date = {2012/07/16},
Citation_Pdf_Url = {http://arxiv.org/pdf/1205.3940},
Citation_Title = {New Directions in Categorical Logic, for Classical, Probabilistic and Quantum Logic},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1205.3940},
Journal = {LMCS},
Title = {New Directions in Categorical Logic, for Classical, Probabilistic and Quantum Logic},
Volume = {(to appear)},
Year = {2012},
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@inproceedings{Jacobs:2011aa,
Abstract = {The expectation monad is introduced abstractly via two composable adjunctions, but concretely captures measures. It turns out to sit in between known monads: on the one hand the distribution and ultrafilter monad, and on the other hand the continuation monad. This expectation monad is used in two probabilistic analogues of fundamental results of Manes and Gelfand for the ultrafilter monad: algebras of the expectation monad are convex compact Hausdorff spaces, and are dually equivalent to so-called Banach effect algebras. These structures capture states and effects in quantum foundations, and also the duality between them. Moreover, the approach leads to a new re-formulation of Gleason's theorem, expressing that effects on a Hilbert space are free effect modules on projections, obtained via tensoring with the unit interval.},
Author = {Bart Jacobs and Jorik Mandemaker},
Booktitle = {Proceedings QPL 2011},
Citation_Arxiv_Id = {1112.3805},
Citation_Author = {Mandemaker, Jorik},
Citation_Date = {2011/12/16},
Citation_Online_Date = {2012/10/02},
Citation_Pdf_Url = {http://arxiv.org/pdf/1112.3805},
Citation_Title = {The Expectation Monad in Quantum Foundations},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.4204/EPTCS.95.12},
Eprint = {arXiv:1112.3805},
Title = {The Expectation Monad in Quantum Foundations},
Year = {2011},
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@unpublished{Dixon:2013aa,
Author = {Lucas Dixon},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Note = {Personal correspondence},
Year = {2013}}
@phdthesis{Merry:2013aa,
Author = {Alexander Merry},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
School = {Oxford University},
Title = {Reasoning with !-graphs},
Year = {2013},
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@book{feynman1994the,
Address = {New York},
Author = {Feynman, Richard},
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Publisher = {Modern Library},
Title = {The character of physical law},
Year = {1994}}
@inproceedings{Lambek:1972aa,
Author = {Joachim Lambek},
Booktitle = {Toposes, Algebraic Geometry and Logic},
Citation_Abstract_Html_Url = {http://link.springer.com/chapter/10.1007/BFb0073965},
Citation_Author = {Joachim Lambek},
Citation_Author_Institution = {Mc Gill University},
Citation_Doi = {10.1007/BFb0073965},
Citation_Firstpage = {57},
Citation_Inbook_Title = {Toposes, Algebraic Geometry and Logic},
Citation_Isbn = {978-3-540-37609-5},
Citation_Language = {en},
Citation_Lastpage = {82},
Citation_Pdf_Url = {http://link.springer.com/content/pdf/10.1007%2FBFb0073965.pdf},
Citation_Publication_Date = {1972/01/01},
Citation_Publisher = {Springer Berlin Heidelberg},
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Citation_Title = {Deductive systems and categories III. Cartesian closed categories, intuitionist propositional calculus, and combinatory logic},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/BFb0073965},
Pages = {57-82},
Publisher = {Springer},
Series = {Lecture Notes in Mathematics},
Title = {Deductive systems and categories III. Cartesian closed categories, intuitionist propositional calculus, and combinatory logic},
Volume = {274},
Year = {1972},
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@article{Cheneau:2012aa,
Abstract = {In relativistic quantum field theory, information propagation is bounded by the speed of light. No such limit exists in the non-relativistic case, although in real physical systems, short-range interactions may be expected to restrict the propagation of information to finite velocities. The question of how fast correlations can spread in quantum many-body systems has been long studied1. The existence of a maximal velocity, known as the Lieb--Robinson bound, has been shown theoretically to exist in several interacting many-body systems (for example, spins on a lattice2, 3, 4, 5)---such systems can be regarded as exhibiting an effective light cone that bounds the propagation speed of correlations. The existence of such a `speed of light' has profound implications for condensed matter physics and quantum information, but has not been observed experimentally. Here we report the time-resolved detection of propagating correlations in an interacting quantum many-body system. By quenching a one-dimensional quantum gas in an optical lattice, we reveal how quasiparticle pairs transport correlations with a finite velocity across the system, resulting in an effective light cone for the quantum dynamics. Our results open perspectives for understanding the relaxation of closed quantum systems far from equilibrium6, and for engineering the efficient quantum channels necessary for fast quantum computations7.},
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Author = {Marc Cheneau and Peter Barmettler and Dario Poletti and Manuel Endres and Peter Schau{\ss} and Takeshi Fukuhara and Christian Gross and Immanuel Bloch and Corinna Kollath and Stefan Kuhr},
Citation_Author = {Stefan Kuhr},
Citation_Date = {2012-01-26},
Citation_Doi = {doi:10.1038/nature10748},
Citation_Firstpage = {484},
Citation_Issue = {7382},
Citation_Journal_Title = {Nature},
Citation_Online_Date = {2012-01-25},
Citation_Publisher = {Nature Publishing Group},
Citation_Title = {Light-cone-like spreading of correlations in a quantum many-body system},
Citation_Volume = {481},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Dc.Date = {2012-01-25},
Dc.Identifier = {doi:10.1038/nature10748},
Dc.Language = {en},
Dc.Rights = {{\copyright} 2012 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
Description = {In relativistic quantum field theory, information propagation is bounded by the speed of light. No such limit exists in the non-relativistic case, although in real physical systems, short-range interactions may be expected to restrict the propagation of information to finite velocities. The question of how fast correlations can spread in quantum many-body systems has been long studied. The existence of a maximal velocity, known as the Lieb-Robinson bound, has been shown theoretically to exist in several interacting many-body systems (for example, spins on a lattice)[mdash]such systems can be regarded as exhibiting an effective light cone that bounds the propagation speed of correlations. The existence of such a /`speed of light/' has profound implications for condensed matter physics and quantum information, but has not been observed experimentally. Here we report the time-resolved detection of propagating correlations in an interacting quantum many-body system. By quenching a one-dimensional quantum gas in an optical lattice, we reveal how quasiparticle pairs transport correlations with a finite velocity across the system, resulting in an effective light cone for the quantum dynamics. Our results open perspectives for understanding the relaxation of closed quantum systems far from equilibrium, and for engineering the efficient quantum channels necessary for fast quantum computations.},
Doi = {10.1038/nature10748},
Emanating = {130X159X184X31},
Journal = {Nature},
Keywords = {Physics},
Pages = {484--487},
Prism.Copyright = {{\copyright} 2012 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
Prism.Eissn = {1476-4687},
Prism.Endingpage = {487},
Prism.Issn = {0028-0836},
Prism.Issue = {7382},
Prism.Publicationdate = {2012-01-25},
Prism.Publicationname = {Nature},
Prism.Rightsagent = {permissions@nature.com},
Prism.Section = {Letter},
Prism.Startingpage = {484},
Prism.Volume = {481},
Publisher = {Nature Publishing Group},
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Title = {Light-cone-like spreading of correlations in a quantum many-body system},
Volume = {481},
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@article{Schaus:2012aa,
Abstract = {The ability to control and tune interactions in ultracold atomic gases has paved the way for the realization of new phases of matter. So far, experiments have achieved a high degree of control over short-range interactions, but the realization of long-range interactions has become a central focus of research because it would open up a new realm of many-body physics. Rydberg atoms are highly suited to this goal because the van der Waals forces between them are many orders of magnitude larger than those between ground-state atoms1. Consequently, mere laser excitation of ultracold gases can cause strongly correlated many-body states to emerge directly when atoms are transferred to Rydberg states. A key example is a quantum crystal composed of coherent superpositions of different, spatially ordered configurations of collective excitations2, 3, 4, 5. Here we use high-resolution, in situ Rydberg atom imaging to measure directly strong correlations in a laser-excited, two-dimensional atomic Mott insulator6. The observations reveal the emergence of spatially ordered excitation patterns with random orientation, but well-defined geometry, in the high-density components of the prepared many-body state. Together with a time-resolved analysis, this supports the description of the system in terms of a correlated quantum state of collective excitations delocalized throughout the gas. Our experiment demonstrates the potential of Rydberg gases to realize exotic phases of matter, thereby laying the basis for quantum simulations of quantum magnets with long-range interactions.},
Access = {Yes},
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Author = {Peter Schau{\ss} and Marc Cheneau and Manuel Endres and Takeshi Fukuhara and Sebastian Hild and Ahmed Omran and Thomas Pohl and Christian Gross and Stefan Kuhr and Immanuel Bloch},
Citation_Author = {Immanuel Bloch},
Citation_Date = {2012-11-01},
Citation_Doi = {doi:10.1038/nature11596},
Citation_Firstpage = {87},
Citation_Issue = {7422},
Citation_Journal_Title = {Nature},
Citation_Online_Date = {2012-10-31},
Citation_Publisher = {Nature Publishing Group},
Citation_Title = {Observation of spatially ordered structures in a two-dimensional Rydberg gas},
Citation_Volume = {491},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Dc.Date = {2012-10-31},
Dc.Identifier = {doi:10.1038/nature11596},
Dc.Language = {en},
Dc.Rights = {{\copyright} 2012 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
Description = {The ability to control and tune interactions in ultracold atomic gases has paved the way for the realization of new phases of matter. So far, experiments have achieved a high degree of control over short-range interactions, but the realization of long-range interactions has become a central focus of research because it would open up a new realm of many-body physics. Rydberg atoms are highly suited to this goal because the van der Waals forces between them are many orders of magnitude larger than those between ground-state atoms. Consequently, mere laser excitation of ultracold gases can cause strongly correlated many-body states to emerge directly when atoms are transferred to Rydberg states. A key example is a quantum crystal composed of coherent superpositions of different, spatially ordered configurations of collective excitations. Here we use high-resolution, in situ Rydberg atom imaging to measure directly strong correlations in a laser-excited, two-dimensional atomic Mott insulator. The observations reveal the emergence of spatially ordered excitation patterns with random orientation, but well-defined geometry, in the high-density components of the prepared many-body state. Together with a time-resolved analysis, this supports the description of the system in terms of a correlated quantum state of collective excitations delocalized throughout the gas. Our experiment demonstrates the potential of Rydberg gases to realize exotic phases of matter, thereby laying the basis for quantum simulations of quantum magnets with long-range interactions.},
Doi = {10.1038/nature11596},
Emanating = {130X159X184X31},
Journal = {Nature},
Keywords = {Physics},
Month = {10},
Pages = {87--91},
Prism.Copyright = {{\copyright} 2012 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
Prism.Eissn = {1476-4687},
Prism.Endingpage = {91},
Prism.Issn = {0028-0836},
Prism.Issue = {7422},
Prism.Publicationdate = {2012-10-31},
Prism.Publicationname = {Nature},
Prism.Rightsagent = {permissions@nature.com},
Prism.Section = {Letter},
Prism.Startingpage = {87},
Prism.Volume = {491},
Publisher = {Nature Publishing Group},
Robots = {noarchive},
Title = {Observation of spatially ordered structures in a two-dimensional Rydberg gas},
Volume = {491},
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@article{Fukuhara:2013aa,
Abstract = {One of the elementary processes in quantum magnetism is the propagation of spin excitations. Here we study the quantum dynamics of a deterministically created spin-impurity atom, as it propagates in a one-dimensional lattice system. We probe the spatial probability distribution of the impurity at different times using single-site-resolved imaging of bosonic atoms in an optical lattice. In the Mott-insulating regime, the quantum-coherent propagation of a magnetic excitation in the Heisenberg model can be observed using a post-selection technique. Extending the study to the superfluid regime of the bath, we quantitatively determine how the bath affects the motion of the impurity, showing evidence of polaronic behaviour. The experimental data agree with theoretical predictions, allowing us to determine the effect of temperature on the impurity motion. Our results provide a new approach to studying quantum magnetism, mobile impurities in quantum fluids and polarons in lattice systems.},
Access = {Yes},
Apple-Itunes-App = {app-id=409367154},
Author = {Takeshi Fukuhara and Adrian Kantian and Manuel Endres and Marc Cheneau and Peter Schau{\ss} and Sebastian Hild and David Bellem and Ulrich Schollw{\"o}ck and Thierry Giamarchi and Christian Gross and Immanuel Bloch and Stefan Kuhr},
Citation_Author = {Stefan Kuhr},
Citation_Date = {2013-04-01},
Citation_Doi = {doi:10.1038/nphys2561},
Citation_Firstpage = {235},
Citation_Issue = {4},
Citation_Journal_Title = {Nature Physics},
Citation_Online_Date = {2013-02-24},
Citation_Publisher = {Nature Publishing Group},
Citation_Title = {Quantum dynamics of a mobile spin impurity},
Citation_Volume = {9},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Dc.Date = {2013-02-24},
Dc.Identifier = {doi:10.1038/nphys2561},
Dc.Language = {en},
Dc.Rights = {{\copyright} 2013 Nature Publishing Group},
Description = {Understanding the propagation of spin excitations is a difficult problem in quantum magnetism. Using site-resolved imaging in a one-dimensional atomic gas, it is possible to track the dynamics of a moving spin impurity through the Mott-insulator and superfluid regimes.},
Doi = {10.1038/nphys2561},
Emanating = {130X159X184X31},
Journal = {Nature Physics},
Keywords = {Atomic and molecular physics, Quantum physics, Condensed-matter physics},
Pages = {235--241},
Prism.Copyright = {{\copyright} 2013 Nature Publishing Group},
Prism.Eissn = {1745-2481},
Prism.Endingpage = {241},
Prism.Issn = {1745-2473},
Prism.Issue = {4},
Prism.Publicationdate = {2013-02-24},
Prism.Publicationname = {Nature Physics},
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Prism.Section = {Article},
Prism.Startingpage = {235},
Prism.Volume = {9},
Publisher = {Nature Publishing Group},
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Title = {Quantum dynamics of a mobile spin impurity},
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@article{Georgescu:2013aa,
Abstract = {Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable or accessible quantum system, i.e., quantum simulation. Quantum simulation promises to have applications in the study of many problems in, e.g., condensed-matter physics, high-energy physics, atomic physics, quantum chemistry and cosmology. Quantum simulation could be implemented using quantum computers, but also with simpler, analog devices that would require less control, and therefore, would be easier to construct. A number of quantum systems such as neutral atoms, ions, polar molecules, electrons in semiconductors, superconducting circuits, nuclear spins and photons have been proposed as quantum simulators. This review outlines the main theoretical and experimental aspects of quantum simulation and emphasizes some of the challenges and promises of this fast-growing field.},
Author = {I. M. Georgescu and S. Ashhab and Franco Nori},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1308.6253},
Journal = {Rev. Mod. Phys.},
Keywords = {quantum computing; quantum simulation;},
Title = {Quantum simulation},
Year = {2013},
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@phdthesis{Kissinger:2012lr,
Author = {Aleks Kissinger},
Citation_Arxiv_Id = {1203.0202},
Citation_Author = {Kissinger, Aleks},
Citation_Date = {2012/03/01},
Citation_Online_Date = {2012/03/22},
Citation_Pdf_Url = {http://arxiv.org/pdf/1203.0202},
Citation_Title = {Pictures of Processes: Automated Graph Rewriting for Monoidal Categories and Applications to Quantum Computing},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1203.0202},
Keywords = {monoidal categories, graphical calculi, rewriting, category theory, categorical quantum mechanics},
School = {Oxford University},
Title = {Pictures of Processes: Automated Graph Rewriting for Monoidal Categories and Applications to Quantum Computing},
Year = {2012},
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@article{Aaronson03isp,
Author = {Scott Aaronson},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Journal = {Bulletin of the European Association for Theoretical Computer Science},
Pages = {109--136},
Title = {Is P versus NP formally independent},
Volume = {81},
Year = {2003},
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@inproceedings{McBride:2005uq,
Author = {Conor McBride},
Booktitle = {Advanced Functional Programming},
Citation_Abstract_Html_Url = {http://link.springer.com/chapter/10.1007/11546382_3},
Citation_Author = {Conor McBride},
Citation_Author_Email = {ctm@cs.nott.ac.uk},
Citation_Author_Institution = {University of Nottingham},
Citation_Doi = {10.1007/11546382_3},
Citation_Firstpage = {130},
Citation_Inbook_Title = {Advanced Functional Programming},
Citation_Isbn = {978-3-540-31872-9},
Citation_Lastpage = {170},
Citation_Pdf_Url = {http://link.springer.com/content/pdf/10.1007%2F11546382_3.pdf},
Citation_Publication_Date = {2005/01/01},
Citation_Publisher = {Springer Berlin Heidelberg},
Citation_Title = {Epigram: Practical Programming with Dependent Types},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/11546382_3},
Format-Detection = {telephone=no},
Pages = {130-170},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {Epigram: Practical Programming with Dependent Types},
Viewport = {width=device-width, minimum-scale=1, maximum-scale=1},
Volume = {3622},
Year = {2005},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/11546382_3}}
@inproceedings{Altenkirch:2006qy,
Author = {Thorsten Altenkirch and Conor McBride and James McKinna},
Booktitle = {Principles of Programming Languages, POPL 2006},
Citation_Authors = {Thorsten Altenkirch, Conor Mcbride, James Mckinna},
Citation_Conference = {In preparation, http://www.e-pig.org/downloads/ydtm.pdf},
Citation_Title = {Why dependent types matter},
Citation_Year = {2005},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Description = {CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We exhibit the rationale behind the design of Epigram, a dependently typed programming language and interactive program development system, using refinements of a well known program---merge sort---as a running example. We discuss its relationship with other proposals to introduce aspects of dependent types into functional programming languages and sketch some topics for further work in this area. 1.},
Doi = {10.1145/1111037.1111038},
Keywords = {dependent types; types},
Title = {Why dependent types matter},
Year = {2006},
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Bdsk-Url-1 = {http://dx.doi.org/10.1145/1111037.1111038}}
@inproceedings{Alexander-S.-Green:2013fk,
Abstract = {The field of quantum algorithms is vibrant. Still, there is currently a lack of programming languages for describing quantum computation on a practical scale, i.e., not just at the level of toy problems. We address this issue by introducing Quipper, a scalable, expressive, functional, higher-order quantum programming language. Quipper has been used to program a diverse set of non-trivial quantum algorithms, and can generate quantum gate representations using trillions of gates. It is geared towards a model of computation that uses a classical computer to control a quantum device, but is not dependent on any particular model of quantum hardware. Quipper has proven effective and easy to use, and opens the door towards using formal methods to analyze quantum algorithms.},
Author = {Alexander S. Green and Peter LeFanu Lumsdaine and Neil J. Ross and Peter Selinger and Beno{\^\i}t Valiron},
Booktitle = {Programming language design and implementation (PLDI'13)},
Citation_Arxiv_Id = {1304.3390},
Citation_Author = {Valiron, Beno{\^\i}t},
Citation_Date = {2013/04/11},
Citation_Online_Date = {2013/04/11},
Citation_Pdf_Url = {http://arxiv.org/pdf/1304.3390},
Citation_Title = {Quipper: A Scalable Quantum Programming Language},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1145/2499370.2462177},
Eprint = {arXiv:1304.3390},
Number = {6},
Pages = {333-342},
Series = {ACM SIGPLAN Notices},
Title = {Quipper: A Scalable Quantum Programming Language},
Volume = {48},
Year = {2013},
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Bdsk-Url-1 = {http://dx.doi.org/10.1145/2499370.2462177}}
@inproceedings{Alexander-S.-Green:2013lr,
Abstract = {Quipper is a recently developed programming language for expressing quantum computations. This paper gives a brief tutorial introduction to the language, through a demonstration of how to make use of some of its key features. We illustrate many of Quipper's language features by developing a few well known examples of Quantum computation, including quantum teleportation, the quantum Fourier transform, and a quantum circuit for addition.},
Author = {Alexander S. Green and Peter LeFanu Lumsdaine and Neil J. Ross and Peter Selinger and Beno{\^\i}t Valiron},
Booktitle = {Reversible Computation (RC2013)},
Citation_Arxiv_Id = {1304.5485},
Citation_Author = {Valiron, Beno{\^\i}t},
Citation_Date = {2013/04/19},
Citation_Online_Date = {2013/04/19},
Citation_Pdf_Url = {http://arxiv.org/pdf/1304.5485},
Citation_Title = {An Introduction to Quantum Programming in Quipper},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/978-3-642-38986-3_10},
Number = {110-124},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {An Introduction to Quantum Programming in Quipper},
Volume = {7948},
Year = {2013},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-38986-3_10}}
@article{Coecke:2013-qpl2012,
Abstract = {We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of finite-dimensional C*-algebras and completely positive maps. In particular, the new category contains both quantum and classical channels, providing elegant abstract notions of preparation and measurement. We also consider nonstandard models, that can be used to investigate which notions from algebraic quantum information theory are operationally justifiable.},
Author = {Bob Coecke and Chris Heunen and Aleks Kissinger},
Citation_Arxiv_Id = {1305.3821},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-10-12 09:09:11 +0000},
Doi = {10.1007/s11128-014-0837-4},
Eprint = {arXiv:1305.3821},
Journal = {Quantum Information Processing},
Pages = {1-31},
Title = {Categories of Quantum and Classical Channels},
Year = {2014},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s11128-014-0837-4}}
@article{:2013lr,
Abstract = {In the categorical approach to the foundations of quantum theory, one begins with a symmetric monoidal category, the objects of which represent physical systems, and the morphisms of which represent physical processes. Usually, this category is taken to be at least compact closed, and more often, dagger compact, enforcing a certain self-duality, whereby preparation processes (roughly, states) are interconvertible with processes of registration (roughly, measurement outcomes). This is in contrast to the more concrete ``operational'' approach, in which the states and measurement outcomes associated with a physical system are represented in terms of what we here call a convex operational model: a certain dual pair of ordered linear spaces--generally, not isomorphic to one another. On the other hand, state spaces for which there is such an isomorphism, which we term weakly self-dual, play an important role in reconstructions of various quantum-information theoretic protocols, including teleportation and ensemble steering. In this paper, we characterize compact closure of symmetric monoidal categories of convex operational models in two ways: as a statement about the existence of teleportation protocols, and as the principle that every process allowed by that theory can be realized as an instance of a remote evaluation protocol---hence, as a form of classical probabilistic conditioning. In a large class of cases, which includes both the classical and quantum cases, the relevant compact closed categories are degenerate, in the weak sense that every object is its own dual. We characterize the dagger-compactness of such a category (with respect to the natural adjoint) in terms of the existence, for each system, of a symmetric bipartite state, the associated conditioning map of which is an isomorphism.},
Author = {Howard Barnum and Ross Duncan and Alexander Wilce},
Citation_Abstract_Html_Url = {http://link.springer.com/article/10.1007/s10992-013-9280-8},
Citation_Author = {Alexander Wilce},
Citation_Author_Email = {wilce@susqu.edu},
Citation_Author_Institution = {Susquehanna University},
Citation_Doi = {10.1007/s10992-013-9280-8},
Citation_Firstpage = {501},
Citation_Fulltext_Html_Url = {http://link.springer.com/article/10.1007/s10992-013-9280-8/fulltext.html},
Citation_Issn = {1573-0433},
Citation_Issue = {3},
Citation_Journal_Abbrev = {J Philos Logic},
Citation_Journal_Title = {Journal of Philosophical Logic},
Citation_Language = {en},
Citation_Lastpage = {523},
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Citation_Publication_Date = {2013/06/01},
Citation_Publisher = {Springer Netherlands},
Citation_Title = {Symmetry, Compact Closure and Dagger Compactness for Categories of Convex Operational Models},
Citation_Volume = {42},
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Journal = {Journal of Philosophical Logic},
Number = {3},
Pages = {501-523},
Title = {Symmetry, Compact Closure and Dagger Compactness for Categories of Convex Operational Models},
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Volume = {42},
Year = {2013},
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@inproceedings{Lang:2011fk,
Author = {Alex Lang and Bob Coecke},
Booktitle = {Proceedings of 8th Workshop on Quantum Physics and Logic (QPL 2011)},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.4204/EPTCS.95.14},
Eprint = {arXiv:1210.0298},
Pages = {193-209},
Series = {Electronic Proceedings in Theoretical Computer Science},
Title = {Trichromatic Open Digraphs for Understanding Qubits},
Volume = {95},
Year = {2011},
Bdsk-Url-1 = {http://dx.doi.org/10.4204/EPTCS.95.14}}
@article{Steane:1996lr,
Abstract = {The concept of multiple-particle interference is discussed, using insights provided by the classical theory of error correcting codes. This leads to a discussion of error correction in a quantum communication channel or a quantum computer. Methods of error correction in the quantum regime are presented, and their limitations assessed. A quantum channel can recover from arbitrary decoherence of x qubits if K bits of quantum information are encoded using n quantum bits, where K/n can be greater than 1 - 2H (2x/n), but must be less than 1 - 2H (x/n). This implies exponential reduction of decoherence with only a polynomial increase in the computing resources required. Therefore quantum computation can be made free of errors in the presence of physically realistic levels of decoherence. The methods also allow isolation of quantum communication from noise and evesdropping (quantum privacy amplification).},
Author = {Andrew Steane},
Citation_Abstract_Html_Url = {http://rspa.royalsocietypublishing.org/content/452/1954/2551.abstract},
Citation_Author = {Andrew Steane},
Citation_Date = {11/08/1996},
Citation_Doi = {10.1098/rspa.1996.0136},
Citation_Firstpage = {2551},
Citation_Id = {452/1954/2551},
Citation_Issn = {1471-2946},
Citation_Issue = {1954},
Citation_Journal_Abbrev = {Proc. R. Soc. Lond. A},
Citation_Journal_Title = {Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences},
Citation_Lastpage = {2577},
Citation_Mjid = {royprsa;452/1954/2551},
Citation_Pdf_Url = {http://rspa.royalsocietypublishing.org/content/452/1954/2551.full.pdf},
Citation_Public_Url = {http://rspa.royalsocietypublishing.org/content/452/1954/2551},
Citation_Title = {Multiple-Particle Interference and Quantum Error Correction},
Citation_Volume = {452},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Dc.Contributor = {Andrew Steane},
Dc.Date = {1996-11-08},
Dc.Format = {text/html},
Dc.Identifier = {10.1098/rspa.1996.0136},
Dc.Language = {en},
Dc.Publisher = {The Royal Society},
Dc.Title = {Multiple-Particle Interference and Quantum Error Correction},
Doi = {10.1098/rspa.1996.0136},
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Keywords = {quantum computing; error correcting codes},
Month = {November},
Number = {1954},
Pages = {2551-2577},
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Title = {Multiple-Particle Interference and Quantum Error Correction},
Volume = {8},
Year = {1996},
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@inproceedings{Backens:2012fk,
Author = {Miriam Backens},
Booktitle = {Proceedings of 9th Workshop on Quantum Physics and Logic (QPL 2012)},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Keywords = {categorical quantum mechanics; quantum computing; measurement-based quantum computing},
Title = {The ZX-calculus is complete for stabilizer quantum mechanics},
Year = {2012}}
@article{Short:2006bh,
Author = {Short, A. J. and Popescu, S. and Gisin, N.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevA.73.012101},
Issue = {1},
Journal = {Phys. Rev. A},
Month = {Jan},
Numpages = {9},
Pages = {012101},
Publisher = {American Physical Society},
Title = {Entanglement swapping for generalized nonlocal correlations},
Url = {http://link.aps.org/doi/10.1103/PhysRevA.73.012101},
Volume = {73},
Year = {2006},
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@article{Popescu:1994qf,
Author = {Sandu Popescu and Daniel Rohrlich},
Citation_Abstract_Html_Url = {http://link.springer.com/article/10.1007/BF02058098},
Citation_Author = {Daniel Rohrlich},
Citation_Author_Institution = {Tel-Aviv University},
Citation_Doi = {10.1007/BF02058098},
Citation_Firstpage = {379},
Citation_Issn = {1572-9516},
Citation_Issue = {3},
Citation_Journal_Abbrev = {Found Phys},
Citation_Journal_Title = {Foundations of Physics},
Citation_Language = {en},
Citation_Lastpage = {385},
Citation_Pdf_Url = {http://link.springer.com/content/pdf/10.1007%2FBF02058098.pdf},
Citation_Publication_Date = {1994/03/01},
Citation_Publisher = {Kluwer Academic Publishers-Plenum Publishers},
Citation_Title = {Quantum nonlocality as an axiom},
Citation_Volume = {24},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/BF02058098},
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Journal = {Foundations of Physics},
Number = {3},
Pages = {379-385},
Title = {Quantum nonlocality as an axiom},
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Volume = {24},
Year = {1994},
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@article{Cirelson:1980ul,
Abstract = {Even though quantum correlations violate Bell's inequality, they satisfy weaker inequalities of a similar type. Some particular inequalities of this kind are proved here. The more general case of instruments located in different space-time regions is also discussed in some detail. Even though quantum correlations violate Bell's inequality, they satisfy weaker inequalities of a similar type. Some particular inequalities of this kind are proved here. The more general case of instruments located in different space-time regions is also discussed in some detail. Even though quantum correlations violate Bell's inequality, they satisfy weaker inequalities of a similar type. Some particular inequalities of this kind are proved here. The more general case of instruments located in different space-time regions is also discussed in some detail.},
Author = {B. S. Cirel'son},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/BF00417500},
Journal = {Letters in Mathematical Physics},
Month = {March},
Number = {2},
Pages = {93-100},
Title = {Quantum generalizations of Bell's inequality},
Volume = {4},
Year = {1980},
Bdsk-Url-1 = {http://dx.doi.org/10.1007/BF00417500}}
@article{Bennett:1996ve,
Author = {Bennett, Charles H. and Brassard, Gilles and Popescu, Sandu and Schumacher, Benjamin and Smolin, John A. and Wootters, William K.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevLett.76.722},
Issue = {5},
Journal = {Phys. Rev. Lett.},
Month = {Jan},
Pages = {722--725},
Publisher = {American Physical Society},
Title = {Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels},
Url = {http://link.aps.org/doi/10.1103/PhysRevLett.76.722},
Volume = {76},
Year = {1996},
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@article{Bennett:1996ly,
Author = {Bennett, Charles H. and Bernstein, Herbert J. and Popescu, Sandu and Schumacher, Benjamin},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevA.53.2046},
Issue = {4},
Journal = {Phys. Rev. A},
Keywords = {quantum computing; entanglement},
Month = {Apr},
Pages = {2046--2052},
Publisher = {American Physical Society},
Title = {Concentrating partial entanglement by local operations},
Url = {http://link.aps.org/doi/10.1103/PhysRevA.53.2046},
Volume = {53},
Year = {1996},
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@phdthesis{Nickau:1996zr,
Author = {Hanno Nickau},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Keywords = {game semantics; programming language; lambda calculus},
School = {Universit{\"a}t Gesamthochschule Siegen},
Title = {Hereditarily Sequential Functionals: A Game Theoretic Approach to Seuqentiality},
Year = {1996},
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@inproceedings{Nickau:1994ys,
Author = {Hanno Nickau},
Booktitle = {Logical Foundations of Computer Science, Third International Symposium, LFCS'94, St. Petersburg, Russia, July 11-14, 1994, Proceedings},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/3-540-58140-5_25},
Editor = {Anil Nerode and Yuri Matiyasevich},
Keywords = {game semantics; lambda calculus; programming language},
Pages = {253-264},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {Hereditarily Sequential Functionals},
Volume = {813},
Year = {1994},
Bdsk-Url-1 = {http://dx.doi.org/10.1007/3-540-58140-5_25}}
@article{Hyland:2000rt,
Author = {J.M.E. Hyland and C.-H.L. Ong},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1006/inco.2000.2917},
Journal = {Information and Computation},
Keywords = {game semantics; programming language; lambda calculus},
Number = {2},
Pages = {285--408},
Robots = {noydir},
Title = {On Full Abstraction for PCF: I, II, and III},
Volume = {163},
Year = {2000},
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Bdsk-Url-1 = {http://dx.doi.org/10.1006/inco.2000.2917}}
@article{Abramsky:2000vn,
Author = {Samson Abramsky and Radha Jagadeesan and Pasquale Malacaria},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1006/inco.2000.2930},
Journal = {Information and Computation},
Keywords = {game semantics; lambda calculus; programming language},
Number = {2},
Pages = {409--470},
Robots = {noydir},
Title = {Full Abstraction for PCF},
Volume = {163},
Year = {2000},
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Bdsk-Url-1 = {http://dx.doi.org/10.1006/inco.2000.2930}}
@article{Brunner:2009yq,
Abstract = {We first present a protocol for deterministically distilling nonlocality, building upon a recent result of Forster et al. [ Phys. Rev. Lett. 102 120401 (2009)]. Our protocol, which is optimal for two-copy distillation, works efficiently for a specific class of postquantum nonlocal boxes, which we term correlated nonlocal boxes. In the asymptotic limit, all correlated nonlocal boxes are distilled to the maximally nonlocal box of Popescu and Rohrlich. Then, taking advantage of a result of Brassard et al. [ Phys. Rev. Lett. 96 250401 (2006)] we show that all correlated nonlocal boxes make communication complexity trivial, and therefore appear very unlikely to exist in nature. Astonishingly, some of these nonlocal boxes are arbitrarily close to the set of classical correlations. This result therefore gives new insight to the problem of why quantum nonlocality is limited.},
Author = {Nicolas Brunner and Paul Skrzypczyk},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevLett.102.160403},
Journal = {Phys. Rev. Lett.},
Number = {160403},
Title = {Nonlocality Distillation and Postquantum Theories with Trivial Communication Complexity},
Volume = {102},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.102.160403}}
@article{Andrew-J.-P.-Garner:2013kx,
Abstract = {Phase plays a crucial role in many quantum effects including interference. Phase is normally defined in terms of complex numbers that appear when representing quantum states as complex vectors. Here we give an operational definition whereby phase is instead defined in terms of measurement statistics. Our definition is phrased in terms of the operational framework known as generalised probabilistic theories, or the convex framework. The definition makes it possible to ask whether other theories in this framework can also have phase. We apply our definition to investigate phase and interference in several example theories: classical probability theory, a version of Spekken's toy model, quantum theory, and box-world. We find that phase is ubiquitous; any non-classical theory can be said to have non-trivial phase dynamics.},
Author = {Andrew J. P. Garner and Oscar C. O. Dahlsten and Yoshifumi Nakata and Mio Murao and Vlatko Vedral},
Citation_Arxiv_Id = {1304.5977},
Citation_Author = {Vedral, Vlatko},
Citation_Date = {2013/04/22},
Citation_Online_Date = {2013/04/22},
Citation_Pdf_Url = {http://arxiv.org/pdf/1304.5977},
Citation_Title = {A general framework for phase and interference},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1304.5977},
Keywords = {alternative physical models; quantum theory},
Title = {A general framework for phase and interference},
Year = {2013},
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@inproceedings{Ghica:2009fj,
Abstract = {After informally reviewing the main concepts from game semantics and placing the development of the field in a historical context we examine its main applications. We focus in particular on finite state model checking, higher order model checking and more recent developments in hardware design.},
Author = {Ghica, D.R.},
Booktitle = {Logic In Computer Science, 2009},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1109/LICS.2009.26},
Keywords = {game semantics},
Pages = {17 - 26},
Title = {Applications of Game Semantics: From Program Analysis to Hardware Synthesis},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1109/LICS.2009.26}}
@article{Danos:2002uq,
Abstract = {A category of HO/N-style games and probabilistic strategies is developed where the possible choices of a strategy are quantified so as to give a measure of the likelihood of seeing a given play. A two-sided die is shown to be universal in this category, in the sense that any strategy breaks down into a composition between some deterministic strategy and that die. The interpretative power of the category is then demonstrated by delineating a Cartesian closed subcategory that provides a fully abstract model of a probabilistic extension of Idealized Algol.},
Author = {Vincent Danos and Russell S. Harmer},
Citation_Abstract_Html_Url = {http://dl.acm.org/citation.cfm?id=507382.507385},
Citation_Authors = {Danos, Vincent; Harmer, Russell S.},
Citation_Date = {07/01/2002},
Citation_Doi = {10.1145/507382.507385},
Citation_Firstpage = {359},
Citation_Issn = {1529-3785},
Citation_Issue = {3},
Citation_Journal_Title = {ACM Transactions on Computational Logic (TOCL)},
Citation_Keywords = {Games semantics; probabilistic Idealized Algol},
Citation_Lastpage = {382},
Citation_Pdf_Url = {http://dl.acm.org/ft_gateway.cfm?id=507385&type=pdf},
Citation_Publisher = {ACM},
Citation_Title = {Probabilistic game semantics},
Citation_Volume = {3},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1145/507382.507385},
Journal = {ACM Transactions on Computational Logic},
Number = {3},
Pages = {359 - 382},
Title = {Probabilistic game semantics},
Volume = {3},
Year = {2002},
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Bdsk-Url-1 = {http://dx.doi.org/10.1145/507382.507385}}
@inproceedings{Kwiatkowska:2010qy,
Abstract = {Probabilistic model checking is a powerful technique for formally verifying quantitative properties of systems that exhibit stochastic behaviour. Such systems are found in many domains: probabilistic behaviour may arise, for example, due to failures of unreliable components, communication across lossy media, or through the use of randomisation in distributed protocols. In this paper, we give a short overview of probabilistic model checking and of PRISM (www.prismmodelchecker.org), currently the leading software tool in this area. We then mention some of the limitations of these techniques, describe some of the advances that are being made to overcome them, and outline key challenges that remain in this research area.},
Author = {Kwiatkowska, M. and Norman, G. and Parker, D.},
Booktitle = {Communication, Control, and Computing (Allerton), 2010},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1109/ALLERTON.2010.5707120},
Keywords = {probabilistic model-checking; probability; process algebra; verification},
Pages = {1691 - 1698},
Title = {Advances and challenges of probabilistic model checking},
Year = {2010},
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Bdsk-Url-1 = {http://dx.doi.org/10.1109/ALLERTON.2010.5707120}}
@article{Ballarini2006125,
Abstract = {It has been recognised for some time that there are close links between the various logics developed for the analysis of multi-agent systems and the many game-theoretic models developed for the same purpose. In this paper, we contribute to this burgeoning body of work by showing how a probabilistic model checking tool can be used for the automated analysis of game-like multi-agent systems in which both agents and environments can act with uncertainty. Specifically, we show how a variation of the well-known alternating offers negotiation protocol of Rubinstein can be encoded as a model for the \{PRISM\} model checker and its behaviour analysed through automatic verification of probabilistic CTL's properties. },
Author = {P. Ballarini and M. Fisher and M.J. Wooldridge},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1016/j.entcs.2005.07.030},
Issn = {1571-0661},
Journal = {Electronic Notes in Theoretical Computer Science},
Keywords = {game theory; probability; automated reasoning; verification},
Note = {<ce:title>Proceedings of the Third Workshop on Model Checking and Artificial Intelligence (MoChArt 2005)</ce:title> <xocs:full-name>Model Checking and Artificial Intelligence 2005</xocs:full-name>},
Number = {2},
Pages = {125 - 137},
Title = {Automated Game Analysis via Probabilistic Model Checking: a case study},
Url = {http://www.sciencedirect.com/science/article/pii/S1571066106000739},
Volume = {149},
Year = {2006},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S1571066106000739},
Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.entcs.2005.07.030}}
@article{Katoen201190,
Abstract = {The Markov Reward Model Checker (MRMC) is a software tool for verifying properties over probabilistic models. It supports \{PCTL\} and \{CSL\} model checking, and their reward extensions. Distinguishing features of \{MRMC\} are its support for computing time- and reward-bounded reachability probabilities, (property-driven) bisimulation minimization, and precise on-the-fly steady-state detection. Recent tool features include time-bounded reachability analysis for continuous-time Markov decision processes (CTMDPs) and \{CSL\} model checking by discrete-event simulation. This paper presents the tool's current status and its implementation details. },
Author = {Joost-Pieter Katoen and Ivan S. Zapreev and Ernst Moritz Hahn and Holger Hermanns and David N. Jansen},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1016/j.peva.2010.04.001},
Issn = {0166-5316},
Journal = {Performance Evaluation},
Keywords = {probability; process algebra; verification; automated reasoning},
Number = {2},
Pages = {90 - 104},
Title = {The ins and outs of the probabilistic model checker \{MRMC\}},
Url = {http://www.sciencedirect.com/science/article/pii/S0166531610000660},
Volume = {68},
Year = {2011},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0166531610000660},
Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.peva.2010.04.001}}
@inproceedings{PRISM:2008fk,
Author = {Mark Kattenbelt and Marta Kwiatkowska and Gethin Norman and David Parker},
Booktitle = {Proceedings of the Sixth Workshop on Quantitative Aspects of Programming Languages (QAPL 2008)},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1016/j.entcs.2008.11.016},
Keywords = {game semantics; probability; process algebra; verification},
Number = {3},
Pages = {5--21},
Robots = {noydir},
Series = {Electronic Notes in Theoretical Computer Science},
Title = {Game-Based Probabilistic Predicate Abstraction in PRISM},
Volume = {220},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.entcs.2008.11.016}}
@inproceedings{Legay:2008lr,
Abstract = {We introduce a simple procedural probabilistic programming language which is suitable for coding a wide variety of randomised algorithms and protocols. This language is interpreted over finite datatypes and has a decidable equivalence problem. We have implemented an automated equivalence checker, which we call apex, for this language, based on game semantics. We illustrate our approach with three non-trivial case studies: (i) Herman's self-stabilisation algorithm; (ii) an analysis of the average shape of binary search trees obtained by certain sequences of random insertions and deletions; and (iii) the problem of anonymity in the Dining Cryptographers protocol. In particular, we record an exponential speed-up in the latter over state-of-the-art competing approaches.},
Author = {Axel Legay and Andrzej S. Murawski and Jo{\"e}l Ouaknine and James Worrell},
Booktitle = {Tools and Algorithms for the Construction and Analysis of Systems (Proc. TACAS 2008)},
Citation_Abstract_Html_Url = {http://link.springer.com/chapter/10.1007/978-3-540-78800-3_13},
Citation_Author = {James Worrell},
Citation_Author_Institution = {Oxford University Computing Laboratory},
Citation_Doi = {10.1007/978-3-540-78800-3_13},
Citation_Firstpage = {173},
Citation_Inbook_Title = {Tools and Algorithms for the Construction and Analysis of Systems},
Citation_Isbn = {978-3-540-78800-3},
Citation_Lastpage = {187},
Citation_Pdf_Url = {http://link.springer.com/content/pdf/10.1007%2F978-3-540-78800-3_13.pdf},
Citation_Publication_Date = {2008/01/01},
Citation_Publisher = {Springer Berlin Heidelberg},
Citation_Title = {On Automated Verification of Probabilistic Programs},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/978-3-540-78800-3_13},
Format-Detection = {telephone=no},
Keywords = {verification; automated reasoning; probability},
Pages = {173-187},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {On Automated Verification of Probabilistic Programs},
Viewport = {width=device-width, minimum-scale=1, maximum-scale=1},
Volume = {4963},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-540-78800-3_13}}
@article{Guiraud:2011zr,
Author = {Yves Guiraud and Philippe Malbos},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Journal = {S{\'e}minaires et Congr{\`e}s},
Pages = {145-161},
Title = {Identities among relations for higher-dimensional rewriting systems},
Volume = {26},
Year = {2011},
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@article{SELINGER:2004fr,
Abstract = {We propose the design of a programming language for quantum computing. Traditionally, quantum algorithms are frequently expressed at the hardware level, for instance in terms of the quantum circuit model or quantum Turing machines. These approaches do not encourage structured programming or abstractions such as data types. In this paper, we describe the syntax and semantics of a simple quantum programming language with high-level features such as loops, recursive procedures, and structured data types. The language is functional in nature, statically typed, free of run-time errors, and has an interesting denotational semantics in terms of complete partial orders of superoperators.},
Author = {Peter Selinger},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Description = {We propose the design of a programming language for quantum computing. Traditionally, quantum algorithms are frequently expressed at the hardware level, for instance in terms of the quantum circuit model or quantum Turing machines. These approaches do not encourage structured programming or abstractions such as data types. In this paper, we describe the syntax and semantics of a simple quantum programming language with high-level features such as loops, recursive procedures, and structured data types. The language is functional in nature, statically typed, free of run-time errors, and has an interesting denotational semantics in terms of complete partial orders of superoperators.},
Doi = {10.1017/S0960129504004256},
Format-Detection = {telephone=no},
Journal = {Mathematical Structures in Computer Science},
Keywords = {quantum computing; categorical quantum mechanics; programming language},
Number = {04},
Pages = {527-586},
Referrer = {default},
Robots = {noodp, noydir},
Test = {displayAbstract},
Title = {Towards a quantum programming language},
Verify-V1 = {P40xFgT/ywJlpV7zP/etM8pJVJZ4CjdOId2dmmiCb+4=},
Volume = {14},
Year = {2004},
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Bdsk-Url-1 = {http://dx.doi.org/10.1017/S0960129504004256}}
@inproceedings{Yoshida:1995ys,
Abstract = {We introduce graph notation for concurrent processes which does not use the notion of port names for its formulation. The operators in the algebra of graphs proposed in this paper are quite different from those in the original term representation, making such notions as connection and correspondence of communication ports explicit. We show how basic elements of process calculi such as agents, reduction, and behavioural equivalences are soundly formulated in the new setting. The work is based on the authors' study on concurrent combinators [9, 10], and can be considered as offering another mathematical representation of the formal notion studied therein.},
Author = {Nobuko Yoshida},
Booktitle = {Theory and Practice of Parallel Programming},
Citation_Abstract_Html_Url = {http://link.springer.com/chapter/10.1007/BFb0026581},
Citation_Author = {Nobuko Yoshida},
Citation_Author_Email = {yoshida@mt.cs.keio.ac.jp},
Citation_Author_Institution = {Keio University},
Citation_Doi = {10.1007/BFb0026581},
Citation_Firstpage = {393},
Citation_Inbook_Title = {Theory and Practice of Parallel Programming},
Citation_Isbn = {978-3-540-49218-4},
Citation_Lastpage = {412},
Citation_Pdf_Url = {http://link.springer.com/content/pdf/10.1007%2FBFb0026581},
Citation_Publication_Date = {1995/01/01},
Citation_Publisher = {Springer Berlin Heidelberg},
Citation_Title = {Graph notation for concurrent combinators},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/BFb0026581},
Format-Detection = {telephone=no},
Keywords = {process algebra; graphical calculi},
Pages = {393-412},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {Graph notation for concurrent combinators},
Viewport = {width=device-width, minimum-scale=1, maximum-scale=1},
Volume = {907},
Year = {1995},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/BFb0026581}}
@article{GADDUCCIa1:2007rt,
Abstract = {We propose a graphical implementation for (possibly recursive) processes of the π-calculus, encoding each process into a graph. Our implementation is sound and complete with respect to the structural congruence for the calculus: two processes are equivalent if and only if they are mapped into graphs with the same normal form. Most importantly, the encoding allows the use of standard graph rewriting mechanisms for modelling the reduction semantics of the calculus.},
Author = {Fabio Gadducci},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Description = {We propose a graphical implementation for (possibly recursive) processes of the π-calculus, encoding each process into a graph. Our implementation is sound and complete with respect to the structural congruence for the calculus: two processes are equivalent if and only if they are mapped into graphs with the same normal form. Most importantly, the encoding allows the use of standard graph rewriting mechanisms for modelling the reduction semantics of the calculus.},
Doi = {10.1017/S096012950700610X},
Format-Detection = {telephone=no},
Journal = {Mathematical Structures in Computer Science},
Keywords = {process algebra; graphical calculi; rewriting},
Number = {03},
Pages = {407-437},
Test = {displayAbstract},
Title = {Graph rewriting for the π-calculus},
Verify-V1 = {P40xFgT/ywJlpV7zP/etM8pJVJZ4CjdOId2dmmiCb+4=},
Volume = {17},
Year = {2007},
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Bdsk-Url-1 = {http://dx.doi.org/10.1017/S096012950700610X}}
@inproceedings{Pattinson:2000vn,
Author = {D. Pattinson},
Booktitle = {Requirements, Design, Correct Construction and Verification},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Editor = {M. V. Cengarle},
Keywords = {coalgebra; rewriting},
Series = {Fast Reihe Softwaretechnik},
Title = {Towards coalgebraic specification of rewrite theories},
Volume = {11},
Year = {2000},
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@inproceedings{Neil-Ghania:2001yq,
Abstract = {Whilst the relationship between initial algebras and monads is well-understood, the relationship between final coalgebras and comonads is less well explored. This paper shows that the problem is more subtle and that final coalgebras can just as easily form monads as comonads and dually, that initial algebras form both monads and comonads.In developing these theories we strive to provide them with an associated notion of syntax. In the case of initial algebras and monads this corresponds to the standard notion of algebraic theories consisting of signatures and equations: models of such algebraic theories are precisely the algebras of the representing monad. We attempt to emulate this result for the coalgebraic case by defining a notion cosignature and coequation and then proving the models of this syntax are precisely the coalgebras of the representing comonad.},
Author = {Neil Ghani and Christoph L{\"u}th and Federico de Marchia and John Power},
Booktitle = {CMCS 2001, Coalgebraic Methods in Computer Science},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1016/S1571-0661(04)80905-8},
Keywords = {category theory; coalgebra; programming language},
Number = {1},
Robots = {noydir},
Title = {Algebras, Coalgebras, Monads and Comonads},
Volume = {44},
Year = {2001},
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Bdsk-Url-1 = {http://dx.doi.org/10.1016/S1571-0661(04)80905-8}}
@inproceedings{Corradini:1999kx,
Author = {Andrea Corradini and Reiko Heckel and Ugo Montanari},
Booktitle = {Fundamentals of Computation Theory},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Keywords = {process algebra; rewriting; coalgebra; category theory},
Pages = {13--38},
Publisher = {Springer},
Series = {LNCS},
Title = {Tile Transition Systems as Structured Coalgebras},
Volume = {1684},
Year = {1999},
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@inproceedings{Kissinger:2012uq,
Abstract = {In recent years, diagrammatic languages have been shown to be a powerful and expressive tool for reasoning about physical, logical, and semantic processes represented as morphisms in a monoidal category. In particular, categorical quantum mechanics, or "Quantum Picturalism", aims to turn concrete features of quantum theory into abstract structural properties, expressed in the form of diagrammatic identities. One way we search for these properties is to start with a concrete model (e.g. a set of linear maps or finite relations) and start composing generators into diagrams and looking for graphical identities. Naively, we could automate this procedure by enumerating all diagrams up to a given size and check for equalities, but this is intractable in practice because it produces far too many equations. Luckily, many of these identities are not primitive, but rather derivable from simpler ones. In 2010, Johansson, Dixon, and Bundy developed a technique called conjecture synthesis for automatically generating conjectured term equations to feed into an inductive theorem prover. In this extended abstract, we adapt this technique to diagrammatic theories, expressed as graph rewrite systems, and demonstrate its application by synthesising a graphical theory for studying entangled quantum states.},
Author = {Aleks Kissinger},
Booktitle = {ATx'12/WInG'12: Joint Proceedings of the Workshops on Automated Theory eXploration and on Invariant Generation, Manchester, UK, June 2012},
Citation_Arxiv_Id = {1202.6079},
Citation_Author = {Kissinger, Aleks},
Citation_Date = {2012/02/27},
Citation_Online_Date = {2012/04/17},
Citation_Pdf_Url = {http://arxiv.org/pdf/1202.6079},
Citation_Title = {Synthesising Graphical Theories},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Editor = {Jacques D. Fleuriot and Peter H{\"o}fner and Annabelle McIver and Alan Smaill},
Eprint = {arXiv:1202.6079},
Series = {EPiC Series},
Title = {Synthesising Graphical Theories},
Volume = {17},
Year = {2012},
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@inproceedings{Lucas-Dixon-University-of-Edinburgh:2010fk,
Abstract = {We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of half-edges (edges which are drawn with an unconnected end) and enjoy rich compositional principles by connecting graphs along these half-edges. In particular, this allows equations and rewrite rules to be specified between graphs. Particular computational models can then be encoded as an axiomatic set of such rules. Further rules can be derived graphically and rewriting can be used to simulate the dynamics of a computational system, e.g. evaluating a program on an input. Examples of models which can be formalised in this way include traditional electronic circuits as well as recent categorical accounts of quantum information.},
Author = {Lucas Dixon and Ross Duncan and Aleks Kissinger},
Booktitle = {Proceedings DCM 2010},
Citation_Arxiv_Id = {1007.3794},
Citation_Author = {Kissinger, Aleks},
Citation_Date = {2010/07/22},
Citation_Online_Date = {2010/07/22},
Citation_Pdf_Url = {http://arxiv.org/pdf/1007.3794},
Citation_Title = {Open Graphs and Computational Reasoning},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.4204/EPTCS.26.16},
Eprint = {arXiv:1006.1937},
Keywords = {category theory; graphical calculi; rewriting},
Pages = {169-180},
Series = {Electronic Proceedings in Theoretical Computer Science},
Title = {Open Graphs and Computational Reasoning},
Volume = {26},
Year = {2010},
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Bdsk-Url-1 = {http://dx.doi.org/10.4204/EPTCS.26.16}}
@inproceedings{Pavlovic:2010lr,
Abstract = {Toy models have been used to separate important features of quantum computation from the rich background of the standard Hilbert space model. Category theory, on the other hand, is a general tool to separate components of mathematical structures, and analyze one layer at a time. It seems natural to combine the two approaches, and several authors have already pursued this idea. We explore *categorical comprehension construction* as a tool for adding features to toy models. We use it to comprehend quantum propositions and probabilities within the basic model of finite-dimensional Hilbert spaces. We also analyze complementary quantum observables over the category of sets and relations. This leads into the realm of *test spaces*, a well-studied model. We present one of many possible extensions of this model, enabled by the comprehension construction. Conspicuously, all models obtained in this way carry the same categorical structure, *extending* the familiar dagger compact framework with the complementation operations. We call the obtained structure *dagger mix autonomous*, because it extends mix autonomous categories, popular in computer science, in a similar way like dagger compact structure extends compact categories. Dagger mix autonomous categories seem to arise quite naturally in quantum computation, as soon as complementarity is viewed as a part of the global structure.},
Author = {Dusko Pavlovic},
Booktitle = {Proceedings of Quantum Physics and Logic, Oxford 8-9 April 2009},
Citation_Arxiv_Id = {1006.1011},
Citation_Author = {Pavlovic, Dusko},
Citation_Date = {2010/06/05},
Citation_Online_Date = {2010/06/05},
Citation_Pdf_Url = {http://arxiv.org/pdf/1006.1011},
Citation_Title = {Relating toy models of quantum computation: comprehension, complementarity and dagger mix autonomous categories},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1006.1011 [},
Keywords = {categorical quantum mechanics; toy models; alternative physical models; quantum computing; monoidal categories},
Title = {Relating toy models of quantum computation: comprehension, complementarity and dagger mix autonomous categories},
Year = {2010},
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@article{Coecke:2008lr,
Abstract = {We recast Selinger's CPM-construction of mixed states completely positive maps [P. Selinger (2007) Dagger compact closed categories and completely positive maps. In: Proceedings of the 3rd International Workshop on Quantum Programming Languages (QPL 2005), Electronic Notes in Theoretical Computer Science 170, 139--163. Available from Peter Selinger's homepage] as an axiomatization of maximally mixed states. This axiomatization also guarantees categories of completely positive maps to satisfy the preparation-state agreement axiom of [Coecke, B. (2007) De-linearizing linearity: projective quantum axiomatics from strong compact closure. In: Proceedings of the 3rd International Workshop on Quantum Programming Languages (QPL 2005), Electronic Notes in Theoretical Computer Science 170, 49--72. E-print: arXiv:quant-ph/0506134], and admits a physical interpretation in terms of purification of mixed states and CPMs. Internal traces, which are crucial in quantum information theory, are the adjoints to these maximally mixed states.},
Author = {Bob Coecke},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1016/j.entcs.2008.04.014},
Journal = {Electronic Notes in Theoretical Computer Science},
Keywords = {categorical quantum mechanics; quantum computing; quantum theory},
Pages = {3--13},
Robots = {noydir},
Title = {Axiomatic Description of Mixed States From Selinger's CPM-construction},
Volume = {210},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.entcs.2008.04.014}}
@article{Chiribella:2008fk,
Abstract = {We present a method for optimizing quantum circuits architecture, based on the notion of a quantum comb, which describes a circuit board where one can insert variable subcircuits. Unexplored quantum processing tasks, such as cloning and storing or retrieving of gates, can be optimized, along with setups for tomography and discrimination or estimation of quantum circuits.},
Author = {G. Chiribella and G. M. D'Ariano and P. Perinotti},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevLett.101.060401},
Journal = {Phys. Rev. Lett},
Keywords = {quantum computing; circuits},
Number = {060401},
Title = {Quantum Circuit Architecture},
Volume = {101},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.101.060401}}
@article{Mottonen:2004lr,
Abstract = {We consider a generic elementary gate sequence which is needed to implement a general quantum gate acting on n qubits---a unitary transformation with 4n degrees of freedom. For synthesizing the gate sequence, a method based on the so-called cosine-sine matrix decomposition is presented. The result is optimal in the number of elementary one-qubit gates, 4n, and scales more favorably than the previously reported decompositions requiring 4n-2n+1 controlled NOT gates.},
Author = {Mikko M{\"o}tt{\"o}nen and Juha J. Vartiainen and Ville Bergholm and Martti M. Salomaa},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevLett.93.130502},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum computing; circuits},
Number = {130502},
Title = {Quantum Circuits for General Multiqubit Gates},
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Author = {David I. Spivak},
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Eprint = {arXiv:1302.6946},
Keywords = {Category Theory},
Publisher = {arXiv.org},
Title = {Category theory for scientists},
Year = {2013},
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@inproceedings{Coecke:2013lr,
Author = {Bob Coecke and Ross Duncan},
Booktitle = {Reversible Computation, 4th International Workshop, RC 2012, Copenhagen, Denmark, July 2-3, 2012.},
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Citation_Author = {Ross Duncan},
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Citation_Publication_Date = {2013/01/01},
Citation_Publisher = {Springer Berlin Heidelberg},
Citation_Title = {Tutorial: Graphical Calculus for Quantum Circuits},
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Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/978-3-642-36315-3_1},
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Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {Tutorial: Graphical Calculus for Quantum Circuits},
Viewport = {width=device-width, minimum-scale=1, maximum-scale=1},
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Year = {2013},
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@article{cite-key,
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Journal = {American Mathematical Monthly},
Month = {August-September},
Number = {7},
Pages = {600-608},
Title = {How to Write a Proof},
Volume = {102},
Year = {1995},
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@inproceedings{Abramsky:2011fj,
Abstract = {A certain class of Frobenius algebras has been used to characterize orthonormal bases and observables on finite-dimensional Hilbert spaces. The presence of units in these algebras means that they can only be realized finite-dimensionally. We seek a suitable generalization, which will allow arbitrary bases and observables to be described within categorical axiomatizations of quantum mechanics. We develop a definition of H*-algebra that can be interpreted in any symmetric monoidal dagger category, reduces to the classical notion from functional analysis in the category of (possibly infinite-dimensional) Hilbert spaces, and hence provides a categorical way to speak about orthonormal bases and quantum observables in arbitrary dimension. Moreover, these algebras reduce to the usual notion of Frobenius algebra in compact categories. We then investigate the relations between nonunital Frobenius algebras and H*-algebras. We give a number of equivalent conditions to characterize when they coincide in the category of Hilbert spaces. We also show that they always coincide in categories of generalized relations and positive matrices.},
Author = {Samson Abramsky and Chris Heunen},
Booktitle = {Clifford Lectures},
Citation_Arxiv_Id = {1011.6123},
Citation_Author = {Heunen, Chris},
Citation_Date = {2010/11/29},
Citation_Online_Date = {2011/07/06},
Citation_Pdf_Url = {http://arxiv.org/pdf/1011.6123},
Citation_Title = {H*-algebras and nonunital Frobenius algebras: first steps in infinite-dimensional categorical quantum mechanics},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-06-18 15:36:57 +0000},
Eprint = {arXiv:1011.6123},
Pages = {1--24},
Series = {AMS Proceedings of Symposia in Applied Mathematics},
Title = {H*-algebras and nonunital Frobenius algebras: first steps in infinite-dimensional categorical quantum mechanics},
Volume = {71},
Year = {2012},
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@article{Abramsky:2011uq,
Abstract = {We use the mathematical language of sheaf theory to give a unified treatment of non-locality and contextuality, in a setting which generalizes the familiar probability tables used in non-locality theory to arbitrary measurement covers; this includes Kochen-Specker configurations and more. We show that contextuality, and non-locality as a special case, correspond exactly to obstructions to the existence of global sections. We describe a linear algebraic approach to computing these obstructions, which allows a systematic treatment of arguments for non-locality and contextuality. We distinguish a proper hierarchy of strengths of no-go theorems, and show that three leading examples --- due to Bell, Hardy, and Greenberger, Horne and Zeilinger, respectively --- occupy successively higher levels of this hierarchy. A general correspondence is shown between the existence of local hidden-variable realizations using negative probabilities, and no-signalling; this is based on a result showing that the linear subspaces generated by the non-contextual and no-signalling models, over an arbitrary measurement cover, coincide. Maximal non-locality is generalized to maximal contextuality, and characterized in purely qualitative terms, as the non-existence of global sections in the support. A general setting is developed for Kochen-Specker type results, as generic, model-independent proofs of maximal contextuality, and a new combinatorial condition is given, which generalizes the `parity proofs' commonly found in the literature. We also show how our abstract setting can be represented in quantum mechanics. This leads to a strengthening of the usual no-signalling theorem, which shows that quantum mechanics obeys no-signalling for arbitrary families of commuting observables, not just those represented on different factors of a tensor product.},
Author = {Samson Abramsky and Adam Brandenburger},
Citation_Arxiv_Id = {1102.0264},
Citation_Author = {Brandenburger, Adam},
Citation_Date = {2011/02/01},
Citation_Online_Date = {2011/11/29},
Citation_Pdf_Url = {http://arxiv.org/pdf/1102.0264},
Citation_Title = {The Sheaf-Theoretic Structure Of Non-Locality and Contextuality},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {doi:10.1088/1367-2630/13/11/113036},
Eprint = {arXiv:1102.0264},
Journal = {New Journal of Physics},
Keywords = {category theory; categorical quantum mechanics; quantum theory; alternative physical models},
Number = {113036},
Title = {The Sheaf-Theoretic Structure Of Non-Locality and Contextuality},
Volume = {13},
Year = {2011},
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Bdsk-Url-1 = {http://dx.doi.org/10.1088/1367-2630/13/11/113036}}
@article{Abramsky:2011fk,
Abstract = {We use a simple relational framework to develop the key notions and results on hidden variables and non-locality. The extensive literature on these topics in the foundations of quantum mechanics is couched in terms of probabilistic models, and properties such as locality and no-signalling are formulated probabilistically. We show that to a remarkable extent, the main structure of the theory, through the major No-Go theorems and beyond, survives intact under the replacement of probability distributions by mere relations.},
Author = {Samson Abramsky},
Citation_Arxiv_Id = {1007.2754},
Citation_Author = {Abramsky, Samson},
Citation_Date = {2010/07/16},
Citation_Online_Date = {2011/10/18},
Citation_Pdf_Url = {http://arxiv.org/pdf/1007.2754},
Citation_Title = {Relational Hidden Variables and Non-Locality},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1007.2754},
Journal = {Studia Logica},
Title = {Relational Hidden Variables and Non-Locality},
Year = {2011},
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@article{Abramsky:2012lr,
Abstract = {A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties which single it out, and the possibilities for alternative theories. Two formalisms which have been used in this context are operational theories, and categorical quantum mechanics. The aim of the present paper is to establish strong connections between these two formalisms. We show how models of categorical quantum mechanics have representations as operational theories. We then show how nonlocality can be formulated at this level of generality, and study a number of examples from this point of view, including Hilbert spaces, sets and relations, and stochastic maps. The local, quantum, and no-signalling models are characterized in these terms.},
Author = {Samson Abramsky and Chris Heunen},
Citation_Arxiv_Id = {1206.0921},
Citation_Author = {Heunen, Chris},
Citation_Date = {2012/06/05},
Citation_Online_Date = {2012/06/06},
Citation_Pdf_Url = {http://arxiv.org/pdf/1206.0921},
Citation_Title = {Operational theories and Categorical quantum mechanics},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1206.0921},
Title = {Operational theories and Categorical quantum mechanics},
Year = {2012},
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@inproceedings{Rannou:2008fj,
Author = {Y. Lafont and P. Rannou},
Booktitle = {Rewriting Techniques and Applications},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Keywords = {rewriting; graphical calculi},
Pages = {232-245},
Series = {Lecture Notes in Computer Science},
Title = {Diagram rewriting for orthogonal matrices: a study of critical peaks},
Volume = {5117},
Year = {2008},
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@article{Lafont:2003qy,
Author = {Y. Lafont},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Journal = {Journal of Pure and Applied Algebra},
Keywords = {graphical calculi; rewriting; category theory},
Number = {2-3},
Pages = {257-310},
Title = {Towards an Algebraic Theory of Boolean Circuits},
Volume = {184},
Year = {2003},
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@article{F.-Metayer:2009fk,
Author = {Y. Lafont and F. M{\'e}tayer},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {http://dx.doi.org/10.1016/j.jpaa.2008.10.005},
Journal = {Journal of Pure and Applied Algebra},
Keywords = {graphical calculi; topology; algebra; rewriting; category theory},
Number = {6},
Pages = {947-968},
Title = {Polygraphic resolutions and homology of monoids},
Volume = {213},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.jpaa.2008.10.005}}
@article{Lafont:2015lr,
Author = {Y. Lafont},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Journal = {Applied Categorical Structures},
Keywords = {graphical calculi; rewriting; category theory},
Pages = {415-437},
Title = {Algebra and geometry of rewriting},
Volume = {15},
Year = {2007},
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@article{Press:2012uq,
Abstract = {The two-player Iterated Prisoner's Dilemma game is a model for both sentient and evolutionary behaviors, especially including the emergence of cooperation. It is generally assumed that there exists no simple ultimatum strategy whereby one player can en- force a unilateral claim to an unfair share of rewards. Here, we show that such strategies unexpectedly do exist. In particular, a player X who is witting of these strategies can (i) deterministi- cally set her opponent Y's score, independently of his strategy or response, or (ii) enforce an extortionate linear relation between her and his scores. Against such a player, an evolutionary player's best response is to accede to the extortion. Only a player with a theory of mind about his opponent can do better, in which case Iterated Prisoner's Dilemma is an Ultimatum Game.},
Author = {William H. Press and Freeman J. Dyson},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1073/pnas.1206569109},
Journal = {PNAS Early Edition},
Title = {Iterated Prisoner's Dilemma contains strategies that dominate any evolutionary opponent},
Year = {2012},
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Bdsk-Url-1 = {http://dx.doi.org/10.1073/pnas.1206569109}}
@article{Eisert:2012fk,
Abstract = {In this work, we show that very natural, apparently simple problems in quantum measurement theory can be undecidable even if their classical analogues are decidable. Undecidability hence appears as a genuine quantum property here. Formally, an undecidable problem is a decision problem for which one cannot construct a single algorithm that will always provide a correct answer in finite time. The problem we consider is to determine whether sequentially used identical Stern-Gerlach-type measurement devices, giving rise to a tree of possible outcomes, have outcomes that never occur. Finally, we point out implications for measurement-based quantum computing and studies of quantum many-body models and suggest that a plethora of problems may indeed be undecidable.},
Author = {J. Eisert and M.P. M\"uller and C. Gogolin},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevLett.108.260501},
Journal = {Phys. Rev. Lett.},
Number = {260501},
Title = {Quantum measurement occurrence is undecidable},
Volume = {108},
Year = {2012},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.108.260501}}
@article{Bell:1964gf,
Author = {J.S. Bell},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Journal = {Physics},
Keywords = {Quantum physics; quantum theory;},
Number = {3},
Title = {On the Einstein Podolsky Rosen paradox},
Volume = {1},
Year = {1964},
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@article{PhysRevLett.49.1804,
Author = {Aspect, Alain and Dalibard, Jean and Roger, G\'erard},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevLett.49.1804},
Issue = {25},
Journal = {Phys. Rev. Lett.},
Keywords = {Quantum physics; quantum theory},
Month = {Dec},
Pages = {1804--1807},
Publisher = {American Physical Society},
Title = {Experimental Test of Bell's Inequalities Using Time- Varying Analyzers},
Url = {http://link.aps.org/doi/10.1103/PhysRevLett.49.1804},
Volume = {49},
Year = {1982},
Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.49.1804},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.49.1804}}
@article{1367-2630-11-4-045018,
Abstract = {We present an approach to the unconditional security of quantum key distribution protocols based on a complementarity argument. The approach is applicable to, but not limited to, every case that has been treated via the argument by Shor and Preskill based on entanglement distillation, with a benefit of decoupling of the error correction from the privacy amplification. It can also treat cases with uncharacterized apparatuses. We derive a secure key rate for the Bennett--Brassard-1984 protocol with an arbitrary source characterized only by a single parameter representing the basis dependence.},
Author = {M. Koashi},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {doi:10.1088/1367-2630/11/4/045018},
Journal = {New Journal of Physics},
Keywords = {quantum computing; mutually unbiased bases},
Number = {4},
Pages = {045018},
Title = {Simple security proof of quantum key distribution based on complementarity},
Url = {http://stacks.iop.org/1367-2630/11/i=4/a=045018},
Volume = {11},
Year = {2009},
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Bdsk-Url-1 = {http://stacks.iop.org/1367-2630/11/i=4/a=045018},
Bdsk-Url-2 = {http://dx.doi.org/10.1088/1367-2630/11/4/045018}}
@article{PhysRevLett.85.441,
Author = {Shor, Peter W. and Preskill, John},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevLett.85.441},
Issue = {2},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum computing;},
Month = {Jul},
Pages = {441--444},
Publisher = {American Physical Society},
Title = {Simple Proof of Security of the BB84 Quantum Key Distribution Protocol},
Url = {http://link.aps.org/doi/10.1103/PhysRevLett.85.441},
Volume = {85},
Year = {2000},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.85.441},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.85.441}}
@article{Kaltenbaek:2010ly,
Abstract = {One-way quantum computation proceeds by sequentially measuring individual spins in an entangled many-spin resource state1. It remains a challenge, however, to efficiently produce such resources. Is it possible to reduce the task of their production to simply cooling a quantum many-body system to its ground state? Cluster states, the canonical resource for one-way quantum computing, do not naturally occur as ground states of physical systems2, 3, leading to a significant effort to identify alternatives that do appear as ground states in spin lattices 4, 5, 6, 7, 8. An appealing candidate is a valence-bond-solid state described by Affleck, Kennedy, Lieb and Tasaki9 (AKLT). It is the unique, gapped ground state for a two-body Hamiltonian on a spin-1 chain, and can be used as a resource for one-way quantum computing 4, 5, 6, 7. Here, we experimentally generate a photonic AKLT state and use it to implement single-qubit quantum logic gates.},
Access = {Yes},
Author = {Rainer Kaltenbaek and Jonathan Lavoie and Bei Zeng and Stephen D. Bartlett and Kevin J. Resch and},
Citation_Authors = {Rainer Kaltenbaek; Jonathan Lavoie; Bei Zeng; Stephen D. Bartlett; Kevin J. Resch},
Citation_Date = {2010-10-17},
Citation_Doi = {doi:10.1038/nphys1777},
Citation_Firstpage = {850},
Citation_Issue = {11},
Citation_Journal_Title = {Nature Physics},
Citation_Publisher = {Nature Publishing Group},
Citation_Title = {Optical one-way quantum computing with a simulated valence-bond solid},
Citation_Volume = {6},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Dc.Date = {2010-10-17},
Dc.Identifier = {doi:10.1038/nphys1777},
Dc.Language = {en},
Dc.Rights = {{\copyright} 2010 Nature Publishing Group},
Description = {One-way quantum computing requires an entangled multiqubit system. So-called cluster states have been proposed to provide this resource, but they are difficult to generate. An alternative that uses the ground state of a one-dimensional chain of spins is now experimentally realized and used to construct a quantum logic gate.},
Doi = {doi:10.1038/nphys1777},
Journal = {Nature Physics},
Keywords = {Quantum physics, Information theory and computation},
Month = {10},
Pages = {850--854},
Prism.Copyright = {{\copyright} 2010 Nature Publishing Group},
Prism.Eissn = {1745-2481},
Prism.Endingpage = {854},
Prism.Issn = {1745-2473},
Prism.Issue = {11},
Prism.Publicationdate = {2010-10-17},
Prism.Publicationname = {Nature Physics},
Prism.Rightsagent = {permissions@nature.com},
Prism.Section = {Letter},
Prism.Startingpage = {850},
Prism.Volume = {6},
Publisher = {Nature Publishing Group},
Robots = {noarchive},
Title = {Optical one-way quantum computing with a simulated valence-bond solid},
Volume = {6},
Wt.Cg_N = {Nature Physics},
Wt.Cg_S = {Letter},
Wt.Template = {C},
Wt.Z_Css = {mobile},
Year = {2010},
Bdsk-Url-1 = {http://dx.doi.org/10.1038/nphys1777}}
@inproceedings{Prince:2008:PPL:1788446.1788459,
Acmid = {1788459},
Address = {Berlin, Heidelberg},
Author = {Prince, Rawle and Ghani, Neil and McBride, Conor},
Booktitle = {Proceedings of the 9th international conference on Functional and logic programming},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Isbn = {3-540-78968-5, 978-3-540-78968-0},
Keywords = {programming language; verification; automated reasoning},
Location = {Ise, Japan},
Numpages = {16},
Pages = {97--112},
Publisher = {Springer-Verlag},
Series = {FLOPS'08},
Title = {Proving properties about lists using containers},
Url = {http://dl.acm.org/citation.cfm?id=1788446.1788459},
Year = {2008},
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Bdsk-Url-1 = {http://dl.acm.org/citation.cfm?id=1788446.1788459}}
@inproceedings{DBLP:conf/cav/KrivineDB09,
Author = {Jean Krivine and Vincent Danos and Arndt Benecke},
Bibsource = {DBLP, http://dblp.uni-trier.de},
Booktitle = {CAV},
Crossref = {DBLP:conf/cav/2009},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Ee = {http://dx.doi.org/10.1007/978-3-642-02658-4_3},
Pages = {17-32},
Title = {Modelling Epigenetic Information Maintenance: A Kappa Tutorial},
Year = {2009},
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@proceedings{DBLP:conf/cav/2009,
Bibsource = {DBLP, http://dblp.uni-trier.de},
Booktitle = {CAV},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Editor = {Ahmed Bouajjani and Oded Maler},
Ee = {http://dx.doi.org/10.1007/978-3-642-02658-4},
Isbn = {978-3-642-02657-7},
Keywords = {verification; automated reasoning},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {Computer Aided Verification, 21st International Conference, CAV 2009, Grenoble, France, June 26 - July 2, 2009. Proceedings},
Volume = {5643},
Year = {2009}}
@inproceedings{DanosEtAl-LICS2010,
Address = {Edinburgh, UK},
Author = {Vincent Danos and J\'er\^ome Feret and Walter Fontana and Russell Harmer and Jean Krivine},
Booktitle = {Proceedings of the Twenty-Fifth Annual IEEE Symposium on Logic in Computer Science, LICS$\,$'2010},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Editor = {{Jean-Pierre} Jouannaud},
Month = {11--14 July},
Pages = {362--381},
Publisher = {IEEE Computer Society},
Title = {Abstracting the differential semantics of rule-based models: exact and automated model reduction},
Volume = {0},
Year = {2010},
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@incollection{gudmund:11c,
Author = {Greg Michaelson and Gudmund Grov},
Booktitle = {Lectures from Central European Functional Programming School},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Publisher = {Springer},
Title = {Reasoning about multi-process systems with the box calculus},
Year = {2011},
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@article{Abramsky:2012mz,
Abstract = {Bell inequalities play a central role in the study of quantum nonlocality and entanglement, with many applications in quantum information. Despite the huge literature on Bell inequalities, it is not easy to find a clear conceptual answer to what a Bell inequality is, or a clear guiding principle as to how they may be derived. In this paper, we introduce a notion of logical Bell inequality which can be used to systematically derive testable inequalities for a very wide variety of situations. There is a single clear conceptual principle, based on purely logical consistency conditions, which underlies our notion of logical Bell inequalities. We show that in a precise sense, all Bell inequalities can be taken to be of this form. Our approach is very general. It applies directly to any family of sets of commuting observables. Thus it covers not only the n-partite scenarios to which Bell inequalities are standardly applied, but also Kochen-Specker configurations, and many other examples. There is much current work on experimental tests for contextuality. Our approach directly yields, in a systematic fashion, testable inequalities for a very general notion of contextuality. There has been much work on obtaining proofs of Bell's theorem ``without inequalities'' or ``without probabilities.'' These proofs are seen as being in a sense more definitive and logically robust than the inequality-based proofs. On the hand, they lack the fault-tolerant aspect of inequalities. Our approach reconciles these aspects, and in fact shows how the logical robustness can be converted into systematic, general derivations of inequalities with provable violations. Moreover, the kind of strong non-locality or contextuality exhibited by the GHZ argument or by Kochen-Specker configurations can be shown to lead to maximal violations of the corresponding logical Bell inequalities. Thus the qualitative and the quantitative aspects are combined harmoniously.},
Author = {Samson Abramsky and Lucien Hardy},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevA.85.062114},
Eprint = {arXiv:1203.1352v6},
Journal = {Phys. Rev. A},
Keywords = {alternative physical models;quantum theory; toposes; logic},
Number = {062114},
Title = {Logical Bell inequalities},
Volume = {85},
Year = {2012},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.85.062114}}
@article{Bob-Coecke:2012zr,
Abstract = {A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This paper is concerned with the encoding of a fixed causal structure within a symmetric monoidal category: causal dependencies will correspond to topological connectedness in the graphical language. We show that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of the concept of a global state forces the monoidal product to be only partially defined, which in turn results in a relativistic covariance theorem. Except for these assumptions, at no stage do we assume anything more than purely compositional symmetric-monoidal categorical structure. We cast these two structural results in terms of a mathematical entity, which we call a causal category. We provide methods of constructing causal categories, and we study the consequences of these methods for the general framework of categorical quantum mechanics.
},
Author = {Bob Coecke and Raymond Lal},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Description = {Bob Coecke, Raymond Lal. Foundations of Physics (14 April 2012), doi:10.1007/s10701-012-9646-8.},
Doi = {10.1007/s10701-012-9646-8},
Eprint = {arXiv:1107.6019},
Journal = {Foundations of Physics},
Keywords = {relativity; alternative physical models; quantum theory; categorical quantum mechanics},
Title = {Causal Categories: Relativistically Interacting Processes},
Year = {2012},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10701-012-9646-8}}
@article{Coecke:2012fr,
Abstract = {There is an incompatibility between the symmetries of causal structure in relativity theory and the signaling abilities of probabilistic devices with inputs and outputs: while time reversal in relativity will not introduce the ability to signal between spacelike separated regions, this is not the case for probabilistic devices with spacelike separated input-output pairs. We explicitly describe a nonsignaling device which becomes a perfect signaling device under time reversal, where time reversal can be conceptualized as playing backwards a videotape of an agent manipulating the device. This leads to an arrow of time that is identifiable when studying the correlations of events for spacelike separated regions. Somewhat surprisingly, although the time reversal of Popescu-Rohrlich boxes also allows agents to signal, it does not yield a perfect signaling device. Finally, we realize time reversal using postselection, which could to lead experimental implementation.},
Author = {Bob Coecke and Raymond Lal},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevLett.108.200403},
Eprint = {arXiv:1108.1988},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum theory; relativity; alternative physical models; categorical quantum mechanics},
Number = {200403},
Title = {Time Asymmetry of Probabilities Versus Relativistic Causal Structure: An Arrow of Time},
Volume = {108},
Year = {2012},
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@inproceedings{Schumacher:2011ys,
Abstract = {We present a discrete model theory similar in structure to ordinary quantum mechanics, but based on a finite field instead of complex amplitudes. The interpretation of this theory involves only the "modal" concepts of possibility and necessity rather than quantitative probability measures. Despite its simplicity, our model theory includes entangled states and has versions of both Bell's theorem and the no cloning theorem.},
Author = {Benjamin Schumacher and Michael D. Westmoreland},
Booktitle = {Proceedings of the 7th Workshop on Quantum Physics and Logic (QPL 2010)},
Citation_Arxiv_Id = {1010.2929},
Citation_Author = {Westmoreland, Michael D.},
Citation_Date = {2010/10/14},
Citation_Online_Date = {2011/08/01},
Citation_Pdf_Url = {http://arxiv.org/pdf/1010.2929},
Citation_Title = {Modal quantum theory},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1010.2929v2},
Keywords = {quantum theory; alternative physical models},
Title = {Modal quantum theory},
Year = {2010},
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@article{Bengtsson:2006rt,
Abstract = {This is a review of the problem of Mutually Unbiased Bases in finite dimensional Hilbert spaces, real and complex. Also a geometric measure of "mubness" is introduced, and applied to some recent calculations in six dimensions (partly done by Bjorck and by Grassl). Although this does not yet solve any problem, some appealing structures emerge.},
Author = {Ingemar Bengtsson},
Citation_Arxiv_Id = {quant-ph/0610216},
Citation_Author = {Bengtsson, Ingemar},
Citation_Date = {2006/10/25},
Citation_Online_Date = {2006/10/25},
Citation_Pdf_Url = {http://arxiv.org/pdf/quant-ph/0610216},
Citation_Title = {Three ways to look at mutually unbiased bases},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:quant-ph/0610216v1},
Keywords = {mutually unbiased bases; quantum theory},
Title = {Three ways to look at mutually unbiased bases},
Year = {2006},
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@article{Mansfield:2012vn,
Abstract = {Hardy's non-locality paradox is a proof without inequalities showing that certain non-local correlations violate local realism. It is `possibilistic' in the sense that one only distinguishes between possible outcomes (positive probability) and impossible outcomes (zero probability). Here we show that Hardy's paradox is quite universal: in any (2,2,l) or (2,k,2) Bell scenario, the occurence of Hardy's paradox is a necessary and sufficient condition for possibilistic non-locality. In particular, it subsumes all ladder paradoxes. This universality of Hardy's paradox is not true more generally: we find a new `proof without inequalities' in the (2,3,3) scenario that can witness non-locality even for correlations that do not display the Hardy paradox. We discuss the ramifications of our results for the computational complexity of recognising possibilistic non-locality.},
Author = {Shane Mansfield and Tobias Fritz},
Citation_Arxiv_Id = {1105.1819},
Citation_Author = {Fritz, Tobias},
Citation_Date = {2011/05/09},
Citation_Online_Date = {2011/05/09},
Citation_Pdf_Url = {http://arxiv.org/pdf/1105.1819},
Citation_Title = {Hardy's Non-locality Paradox and Possibilistic Conditions for Non-locality},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/s10701-012-9640-1},
Eprint = {arXiv:1105.1819},
Journal = {Foundations of Physics},
Keywords = {quantum theory; alternative physical models},
Number = {5},
Pages = {709-719},
Title = {Hardy's Non-locality Paradox and Possibilistic Conditions for Non-locality},
Volume = {42},
Year = {2012},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10701-012-9640-1}}
@inproceedings{Abramsky:2011yq,
Abstract = {In a previous paper with Adam Brandenburger, we used sheaf theory to analyze the structure of non-locality and contextuality. Moreover, on the basis of this formulation, we showed that the phenomena of non-locality and contextuality can be characterized precisely in terms of obstructions to the existence of global sections. Our aim in the present work is to build on these results, and to use the powerful tools of sheaf cohomology to study the structure of non-locality and contextuality. We use the Cech cohomology on an abelian presheaf derived from the support of a probabilistic model, viewed as a compatible family of distributions, in order to define a cohomological obstruction for the family as a certain cohomology class. This class vanishes if the family has a global section. Thus the non-vanishing of the obstruction provides a sufficient (but not necessary) condition for the model to be contextual. We show that for a number of salient examples, including PR boxes, GHZ states, and the 18-vector configuration due to Cabello et al. giving a proof of the Kochen-Specker theorem in four dimensions, the obstruction does not vanish, thus yielding cohomological witnesses for contextuality.},
Author = {Samson Abramsky and Shane Mansfield and Rui Soares Barbosa},
Booktitle = {Proceedings of QPL 2011},
Citation_Arxiv_Id = {1111.3620},
Citation_Author = {Barbosa, Rui Soares},
Citation_Date = {2011/11/15},
Citation_Online_Date = {2011/11/15},
Citation_Pdf_Url = {http://arxiv.org/pdf/1111.3620},
Citation_Title = {The Cohomology of Non-Locality and Contextuality},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1111.3620v1},
Keywords = {alternative physical models; categorical quantum mechanics; topology; algebra},
Series = {Electronic Proceedings in Theoretical Computer Science},
Title = {The Cohomology of Non-Locality and Contextuality},
Year = {2011},
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@article{Masanes:2011kx,
Abstract = {Quantum theory (QT) is usually formulated in terms of abstract mathematical postulates involving Hilbert spaces, state vectors and unitary operators. In this paper, we show that the full formalism of QT can instead be derived from five simple physical requirements, based on elementary assumptions regarding preparations, transformations and measurements. This is very similar to the usual formulation of special relativity, where two simple physical requirements---the principles of relativity and light speed invariance---are used to derive the mathematical structure of Minkowski space--time. Our derivation provides insights into the physical origin of the structure of quantum state spaces (including a group-theoretic explanation of the Bloch ball and its three dimensionality) and suggests several natural possibilities to construct consistent modifications of QT.},
Author = {Llu{\'\i}s Masanes and Markus P M{\"u}ller},
Citation_Abstract_Html_Url = {http://iopscience.iop.org/1367-2630/13/6/063001},
Citation_Author = {Markus P M{\"u}ller},
Citation_Author_Institution = {Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, ON, N2L 2Y5, Canada},
Citation_Doi = {10.1088/1367-2630/13/6/063001},
Citation_Firstpage = {063001},
Citation_Fulltext_Html_Url = {http://iopscience.iop.org/1367-2630/13/6/063001/fulltext/},
Citation_Issn = {1367-2630},
Citation_Issue = {6},
Citation_Journal_Abbrev = {New J. Phys.},
Citation_Journal_Title = {New Journal of Physics},
Citation_Language = {en},
Citation_Pdf_Url = {http://iopscience.iop.org/1367-2630/13/6/063001/pdf/1367-2630_13_6_063001.pdf},
Citation_Publication_Date = {2011-06-01},
Citation_Publisher = {IOP Publishing},
Citation_Title = {A derivation of quantum theory from physical requirements},
Citation_Volume = {13},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Dc.Creator = {Markus P M{\"u}ller},
Dc.Date = {2011-06-01},
Dc.Description = {Quantum theory (QT) is usually formulated in terms of abstract mathematical postulates involving Hilbert spaces, state vectors and unitary operators. In this paper, we show that the full formalism of QT can instead be derived from five simple physical requirements, based on elementary assumptions regarding preparations, transformations and measurements. This is very similar to the usual formulation of special relativity, where two simple physical requirements---the principles of relativity and light speed invariance---are used to derive the mathematical structure of Minkowski space--time. Our derivation provides insights into the physical origin of the structure of quantum state spaces (including a group-theoretic explanation of the Bloch ball and its three dimensionality) and suggests several natural possibilities to construct consistent modifications of QT.},
Dc.Format = {text/html},
Dc.Identifier = {10.1088/1367-2630/13/6/063001},
Dc.Language = {en},
Dc.Publisher = {IOP Publishing},
Dc.Title = {A derivation of quantum theory from physical requirements},
Dc.Type = {Text},
Description = {Quantum theory (QT) is usually formulated in terms of abstract mathematical postulates involving Hilbert spaces, state vectors and unitary operators. In this paper, we show that the full formalism of QT can instead be derived from five simple physical requirements, based on elementary assumptions regarding preparations, transformations and measurements. This is very similar to the usual formulation of special relativity, where two simple physical requirements---the principles of relativity and light speed invariance---are used to derive the mathematical structure of Minkowski space--time. Our derivation provides insights into the physical origin of the structure of quantum state spaces (including a group-theoretic explanation of the Bloch ball and its three dimensionality) and suggests several natural possibilities to construct consistent modifications of QT.},
Doi = {10.1088/1367-2630/13/6/063001},
Journal = {New Journal of Physics},
Keywords = {quantum theory; alternative physical models},
Number = {063001},
Robots = {noarchive},
Title = {A derivation of quantum theory from physical requirements},
Volume = {13},
Year = {2011},
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@incollection{Dakic:2011fj,
Abstract = {Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some features with quantum theory, such as probabilistic predictions for individual outcomes (indeterminism), the impossibility of information transfer faster than speed of light (no-signaling) or the impossibility of copying of unknown states (no-cloning). A vast majority of attempts to find physical principles behind quantum theory either fall short of deriving the theory uniquely from the principles or are based on abstract mathematical assumptions that require themselves a more conclusive physical motivation. Here, we show that classical probability theory and quantum theory can be reconstructed from three reasonable axioms: (1) (Information capacity) All systems with information carrying capacity of one bit are equivalent. (2) (Locality) The state of a composite system is completely determined by measurements on its subsystems. (3) (Reversibility) Between any two pure states there exists a reversible transformation. If one requires the transformation from the last axiom to be continuous, one separates quantum theory from the classical probabilistic one. A remarkable result following from our reconstruction is that no probability theory other than quantum theory can exhibit entanglement without contradicting one or more axioms.},
Author = {Borivoje Dakic and Caslav Brukner},
Booktitle = {Deep Beauty: Understanding the Quantum World through Mathematical Innovation},
Citation_Arxiv_Id = {0911.0695},
Citation_Author = {Brukner, Caslav},
Citation_Date = {2009/11/03},
Citation_Online_Date = {2009/11/03},
Citation_Pdf_Url = {http://arxiv.org/pdf/0911.0695},
Citation_Title = {Quantum Theory and Beyond: Is Entanglement Special?},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Editor = {H. Halvorson},
Eprint = {arXiv:0911.0695v1},
Keywords = {quantum theory; alternative physical models; entanglement},
Publisher = {Cambridge University Press},
Title = {Quantum Theory and Beyond: Is Entanglement Special?},
Year = {2011},
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@article{Chiribella:2011uq,
Abstract = {We derive quantum theory from purely informational principles. Five elementary axioms---causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning---define a broad class of theories of information processing that can be regarded as standard. One postulate---purification---singles out quantum theory within this class.},
Author = {Giulio Chiribella and Giacomo Mauro D'Ariano and Paolo Perinotti},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevA.84.012311},
Eprint = {arXiv:1011.6451v3},
Journal = {Phys. Rev. A},
Keywords = {quantum theory; alternative physical models},
Number = {012311},
Title = {Informational derivation of quantum theory},
Volume = {84},
Year = {2011},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.84.012311}}
@mastersthesis{Hillebrand:2011qy,
Author = {Anne Hillebrand},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Keywords = {categorical quantum mechanics; quantum computing; graphical calculi; rewriting;},
School = {Oxford University},
Title = {Quantum Protocols involving Multiparticle Entanglement and their Representations in the {ZX}-calculus},
Year = {2011},
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@article{Coecke:2012lr,
Abstract = {We introduce a graphical framework for Bayesian inference that is sufficiently general to accommodate not just the standard case but also recent proposals for a theory of quantum Bayesian inference wherein one considers density operators rather than probability distributions as representative of degrees of belief. The diagrammatic framework is stated in the graphical language of symmetric monoidal categories and of compact structures and Frobenius structures therein, in which Bayesian inversion boils down to transposition with respect to an appropriate compact structure. We characterize classical Bayesian inference in terms of a graphical property and demonstrate that our approach eliminates some purely conventional elements that appear in common representations thereof, such as whether degrees of belief are represented by probabilities or entropic quantities. We also introduce a quantum-like calculus wherein the Frobenius structure is noncommutative and show that it can accommodate Leifer's calculus of `conditional density operators'. The notion of conditional independence is also generalized to our graphical setting and we make some preliminary connections to the theory of Bayesian networks. Finally, we demonstrate how to construct a graphical Bayesian calculus within any dagger compact category.},
Audience = {all},
Author = {Bob Coecke and Robert W. Spekkens},
Copyright = {2011 - Springer},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Distribution = {GLOBAL},
Doi = {10.1007/s11229-011-9917-5},
Eprint = {arXiv:1102.2368v1},
Journal = {Synthese},
Keywords = {quantum theory; categorical quantum mechanics; alternative physical models; probability},
Number = {3},
Pages = {651-696},
Title = {Picturing classical and quantum Bayesian inference},
Volume = {186},
Year = {2012},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s11229-011-9917-5}}
@incollection{Duncan:2012uq,
Abstract = {Quantum computations are easily represented in the graphical notation known as the ZX-calculus, a.k.a. the red-green calculus. We demonstrate its use in reasoning about measurement-based quantum computing, where the graphical syntax directly captures the structure of the entangled states used to represent computations, and show that the notion of information flow within the entangled states gives rise to rewriting strategies for proving the correctness of quantum programs.},
Author = {Ross Duncan},
Booktitle = {Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse},
Chapter = {3},
Citation_Arxiv_Id = {1203.6242},
Citation_Author = {Duncan, Ross},
Citation_Date = {2012/03/28},
Citation_Online_Date = {2012/03/28},
Citation_Pdf_Url = {http://arxiv.org/pdf/1203.6242},
Citation_Title = {A graphical approach to measurement-based quantum computing},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Editor = {Chris Heunen and Mehrnoosh Sadrzadeh and Edward Grefenstette},
Eprint = {arxiv:1203.6242},
Isbn = {978-0-19-964629-6},
Keywords = {categorical quantum mechanics; quantum computing; measurement-based quantum computing},
Publisher = {Oxford University Press},
Title = {A graphical approach to measurement-based quantum computing},
Year = {2013},
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@inproceedings{CDKW-lics:2012qy,
Abstract = {Categorical quantum mechanics studies quantum theory in the framework of dagger-compact closed categories. Using this framework, we establish a tight relationship between two key quantum theoretical notions: non-locality and complementarity. In particular, we establish a direct connection between Mermin-type non-locality scenarios, which we generalise to an arbitrary number of parties, using systems of arbitrary dimension, and performing arbitrary measurements, and a new stronger notion of complementarity which we introduce here. Our derivation of the fact that strong complementarity is a necessary condition for a Mermin scenario provides a crisp operational interpretation for strong complementarity. We also provide a complete classification of strongly complementary observables for quantum theory, something which has not yet been achieved for ordinary complementarity. Since our main results are expressed in the (diagrammatic) language of dagger-compact categories, they can be applied outside of quantum theory, in any setting which supports the purely algebraic notion of strongly complementary observables. We have therefore introduced a method for discussing non-locality in a wide variety of models in addition to quantum theory. The diagrammatic calculus substantially simplifies (and sometimes even trivialises) many of the derivations, and provides new insights. In particular, the diagrammatic computation of correlations clearly shows how local measurements interact to yield a global overall effect. In other words, we depict non-locality.},
Author = {Bob Coecke and Ross Duncan and Aleks Kissinger and Quanlong Wang},
Booktitle = {Proceedings of the 27th Annual IEEE Symposium on Logic in Computer Science. (LiCS2012)},
Citation_Arxiv_Id = {1203.4988},
Citation_Author = {Wang, Quanlong},
Citation_Date = {2012/03/22},
Citation_Online_Date = {2012/04/27},
Citation_Pdf_Url = {http://arxiv.org/pdf/1203.4988},
Citation_Title = {Strong Complementarity and Non-locality in Categorical Quantum Mechanics},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1109/LICS.2012.35},
Eprint = {arXiv:1203.4988},
Keywords = {categorical quantum mechanics; alternative physical models; quantum theory},
Pages = {245--254},
Publisher = {IEEE Computer Society Press},
Title = {Strong Complementarity and Non-locality in Categorical Quantum Mechanics},
Year = {2012},
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@article{Bob-Coecke:2010fk,
Abstract = {We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, for which we rely on the algebra of Pregroups, introduced by Lambek. This mathematical framework enables us to compute the meaning of a well-typed sentence from the meanings of its constituents. Concretely, the type reductions of Pregroups are `lifted' to morphisms in a category, a procedure that transforms meanings of constituents into a meaning of the (well-typed) whole. Importantly, meanings of whole sentences live in a single space, independent of the grammatical structure of the sentence. Hence the inner-product can be used to compare meanings of arbitrary sentences, as it is for comparing the meanings of words in the distributional model. The mathematical structure we employ admits a purely diagrammatic calculus which exposes how the information flows between the words in a sentence in order to make up the meaning of the whole sentence. A variation of our `categorical model' which involves constraining the scalars of the vector spaces to the semiring of Booleans results in a Montague-style Boolean-valued semantics.},
Author = {Bob Coecke and Mehrnoosh Sadrzadeh and Stephen Clark},
Citation_Arxiv_Id = {1003.4394},
Citation_Author = {Clark, Stephen},
Citation_Date = {2010/03/23},
Citation_Online_Date = {2010/03/23},
Citation_Pdf_Url = {http://arxiv.org/pdf/1003.4394},
Citation_Title = {Mathematical Foundations for a Compositional Distributional Model of Meaning},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2016-07-27 17:16:38 +0000},
Eprint = {arXiv:1003.4394v1},
Journal = {Linguistic Analysis},
Keywords = {linguistics; compact closed categories},
Title = {Mathematical Foundations for a Compositional Distributional Model of Meaning},
Volume = {36},
Year = {2010},
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@article{Verstraete:2008lr,
Abstract = {This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected entangled pair states.},
Author = {F. Verstraete and J.I. Cirac and V. Murg},
Citation_Arxiv_Id = {0907.2796},
Citation_Author = {Murg, V.},
Citation_Date = {2009/07/16},
Citation_Online_Date = {2009/07/16},
Citation_Pdf_Url = {http://arxiv.org/pdf/0907.2796},
Citation_Title = {Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1080/14789940801912366},
Eprint = {arXiv:0907.2796},
Journal = {Adv. Phys.},
Keywords = {quantum computing; quantum many-body},
Number = {143},
Title = {Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems},
Volume = {57},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1080/14789940801912366}}
@article{Mermin:1998fk,
Author = {N. David Mermin},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1119/1.18955},
Eprint = {quant-ph/9801057},
Journal = {American Journal of Physics},
Keywords = {quantum theory; alternative physical models},
Number = {9},
Pages = {453},
Title = {What is quantum mechanics trying to tell us?},
Volume = {66},
Year = {1998},
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Bdsk-Url-1 = {http://dx.doi.org/10.1119/1.18955}}
@article{Mermin:1990fk,
Author = {N. David Mermin},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1119/1.16503},
Journal = {American Journal of Physics},
Keywords = {quantum theory; alternative physical models},
Number = {8},
Pages = {731-734},
Title = {Quantum Mysteries Revisited},
Volume = {58},
Year = {1990},
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@article{HFDM-2012,
Abstract = {In recent years, surface codes have become a leading method for quantum error correction in theoretical large-scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural two-dimensional nearest-neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally realistic systems. While fundamentally based on the toric code of Kitaev, there are many variants, two of which are the planar- and defect-based codes. Planar codes require fewer qubits to implement (for the same strength of error correction), but are restricted to encoding a single qubit of information. Interactions between encoded qubits are achieved via transversal operations, thus destroying the inherent 2DNN nature of the code. In this paper we introduce a new technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN of the encoded computer. Our lattice surgery technique comprises splitting and merging planar code surfaces, and enables us to perform universal quantum computation (including magic state injection) while removing the need for braided logic in a strictly 2DNN design, and hence reduces the overall qubit resources for logic operations. Those resources are further reduced by the use of a rotated lattice for the planar encoding. We show how lattice surgery allows us to distribute encoded GHZ states in a more direct (and overhead friendly) manner, and how a demonstration of an encoded CNOT between two distance-3 logical states is possible with 53 physical qubits, half of that required in any other known construction in 2D.},
Author = {Clare Horsman and Austin G Fowler and Simon Devitt and Rodney Van Meter},
Journal = {New Journal of Physics},
Number = {12},
Pages = {123011},
Title = {Surface code quantum computing by lattice surgery},
Url = {http://stacks.iop.org/1367-2630/14/i=12/a=123011},
Volume = {14},
Year = {2012},
Bdsk-Url-1 = {http://stacks.iop.org/1367-2630/14/i=12/a=123011}}
@article{HND-2017,
Abstract = {In this paper we outline a method for a compiler to translate any non fault tolerant quantum circuit to the geometric representation of the lattice surgery error-correcting code using inherent merge and split operations. Since the efficiency of state distillation procedures has not yet been investigated in the lattice surgery model, their translation is given as an example using the proposed method. The resource requirements seem comparable or better to the defect-based state distillation process, but modularity and eventual implementability allow the lattice surgery model to be an interesting alternative to braiding.},
Author = {Daniel Herr and Franco Nori and Simon J Devitt},
Journal = {New Journal of Physics},
Number = {1},
Pages = {013034},
Title = {Lattice surgery translation for quantum computation},
Url = {http://stacks.iop.org/1367-2630/19/i=1/a=013034},
Volume = {19},
Year = {2017},
Bdsk-Url-1 = {http://stacks.iop.org/1367-2630/19/i=1/a=013034}}
@misc{Bob-Coecke:2011lr,
Abstract = {We provide two mathematical descriptions of Spekkens's toy qubit theory, an inductively one in terms of a small set of generators, as well as an explicit closed form description. It is a subcategory MSpek of the category of finite sets, relations and the cartesian product. States of maximal knowledge form a subcategory Spek. This establishes the consistency of the toy theory, which has previously only been constructed for at most four systems. Our model also shows that the theory is closed under both parallel and sequential composition of operations (= symmetric monoidal structure), that it obeys map-state duality (= compact closure), and that states and effects are in bijective correspondence (= dagger structure). From the perspective of categorical quantum mechanics, this provides an interesting alternative model which enables us to describe many quantum phenomena in a discrete manner, and to which mathematical concepts such as basis structures, and complementarity thereof, still apply. Hence, the framework of categorical quantum mechanics has delivered on its promise to encompass theories other than quantum theory.},
Author = {Bob Coecke and Bill Edwards},
Citation_Arxiv_Id = {1108.1978},
Citation_Author = {Edwards, Bill},
Citation_Date = {2011/08/09},
Citation_Online_Date = {2011/08/09},
Citation_Pdf_Url = {http://arxiv.org/pdf/1108.1978},
Citation_Title = {Spekkens's toy theory as a category of processes},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1108.1978},
Keywords = {alternative physical models; quantum theory; categorical quantum mechanics},
Title = {Spekkens's toy theory as a category of processes},
Year = {2011},
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@book{Kaye:2007qy,
Author = {Phillip Kaye and Raymond Laflamme and Michele Mosca},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Description = {This concise, accessible text provides a thorough introduction to quantum computing - an exciting emergent field at the interface of the computer, engineering, mathematical and physical sciences. Aimed at advanced undergraduate and beginning graduate students in these disciplines, the text is technically detailed and is clearly illustrated throughout with diagrams and exercises. Some prior knowledge of linear algebra is assumed, including vector spaces and inner products. However, prior familiarity with topics such as tensor products and spectral decomposition is not required, as the necessary material is reviewed in the text.},
Keywords = {quantum computing},
Publisher = {Oxford University Press},
Title = {An introduction to quantum computing},
Year = {2007}}
@book{Mermin:2007fk,
Abstract = {In the 1990's it was realized that quantum physics has some spectacular applications in computer science. This book is a concise introduction to quantum computation, developing the basic elements of this new branch of computational theory without assuming any background in physics. It begins with an introduction to the quantum theory from a computer-science perspective. It illustrates the quantum-computational approach with several elementary examples of quantum speed-up, before moving to the major applications: Shor's factoring algorithm, Grover's search algorithm, and quantum error correction. The book is intended primarily for computer scientists who know nothing about quantum theory, but will also be of interest to physicists who want to learn the theory of quantum computation, and philosophers of science interested in quantum foundational issues. It evolved during six years of teaching the subject to undergraduates and graduate students in computer science, mathematics, engineering, and physics, at Cornell University.},
Author = {N. David Mermin},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Isbn = {9780521876582},
Keywords = {quantum computing},
Publisher = {Cambridge University Press},
Title = {Quantum Computer Science},
Year = {2007}}
@article{Fritz:2012lr,
Abstract = {In quantum mechanics, nonlocality (a violation of a Bell inequality) is intimately linked to complementarity, by which we mean that consistently assigning values to different observables at the same time is not possible. Nonlocality can only occur when some of the relevant observables do not commute, and this noncommutativity makes the observables complementary. Beyond quantum mechanics, the concept of complementarity can be formalized in several distinct ways. Here we describe some of these possible formalizations and ask how they relate to nonlocality. We partially answer this question by describing two toy theories which display nonlocality and obey the no-signaling principle, although each of them does not display a certain kind of complementarity. The first toy theory has the property that it maximally violates the Clauser, Horn, Shimony, and Holt (CHSH) inequality, although the corresponding local observables are pairwise jointly measurable. The second toy theory also maximally violates the CHSH inequality, although its state space is classical and all measurements are mutually nondisturbing: if a measurement sequence contains some measurement twice with any number of other measurements in between, then these two measurements give the same outcome with certainty.},
Author = {Tobias Fritz},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevA.85.022102},
Journal = {Phys. Rev. A},
Keywords = {alternative physical models; quantum theory; mutually unbiased bases},
Number = {022102},
Title = {Nonlocality with less complementarity},
Volume = {85},
Year = {2012},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.85.022102}}
@inproceedings{Panangaden:2011lr,
Abstract = {I give a non-comprehensive survey of the categorical quantum mechanics program and how it guides the search for structure in quantum computation. I discuss the example of measurement-based computing which is one of the successes of such an enterprise and briefly mention topological quantum computing which is an inviting target for future research in this area.},
Audience = {all},
Author = {Prakash Panangaden},
Booktitle = {Foundations of Software Science and Computational Structures FOSSACS 2011},
Copyright = {2011 - Springer},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Distribution = {GLOBAL},
Doi = {10.1007/978-3-642-19805-2_1},
Editor = {Martin Hofmann},
Keywords = {quantum computing},
Pages = {1-11},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {The Search for Structure in Quantum Computation},
Volume = {6604},
Year = {2011},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-19805-2_1}}
@article{Abramsky:2009lr,
Abstract = {Recently, the author and Bob Coecke have introduced a categorical formulation of Quantum Mechanics. In the present paper, we shall use it to open up a novel perspective on No-Cloning. What we shall find, quite unexpectedly, is a link to some fundamental issues in logic, computation, and the foundations of mathematics. A striking feature of our results is that they are visibly in the same genre as a well-known result by Joyal in categorical logic showing that a `Boolean cartesian closed category' trivializes, which provides a major road-block to the computational interpretation of classical logic. In fact, they strengthen Joyal's result, insofar as the assumption of a full categorical product (both diagonals and projections) in the presence of a classical duality is weakened. This shows a heretofore unsuspected connection between limitative results in proof theory and No-Go theorems in quantum mechanics.},
Author = {Samson Abramsky},
Citation_Arxiv_Id = {0910.2401},
Citation_Author = {Abramsky, Samson},
Citation_Date = {2009/10/13},
Citation_Online_Date = {2009/10/13},
Citation_Pdf_Url = {http://arxiv.org/pdf/0910.2401},
Citation_Title = {No-Cloning In Categorical Quantum Mechanics},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:0910.2401v1},
Keywords = {categorical quantum mechanics; alternative physical models; monoidal categories},
Title = {No-Cloning In Categorical Quantum Mechanics},
Year = {2009},
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@article{Horsman:2011lr,
Abstract = {Topological quantum computing (QC) is a way of allowing precise quantum computations to run on noisy and imperfect hardware. One implementation uses surface codes created by forming defects in a highly-entangled cluster state. Such a method of computing is a leading candidate for large-scale QC. However, there has been a lack of sufficiently powerful high-level languages to describe computing in this form without resorting to single-qubit operations, which quickly become prohibitively complex as the system size increases. In this paper, we apply the category-theoretic work of Abramsky and Coecke to the topological cluster-state model of QC to give a high-level graphical language that enables direct translation between quantum processes and physical patterns of measurement in a computer---a 'compiler language'. We give the equivalence between the graphical and topological information flows, and show the applicable rewrite algebra for this computing model. We show that this gives us a native graphical language for the design and analysis of topological quantum algorithms, and finish by discussing the possibilities for automating this process on a large scale.},
Author = {Clare Horsman},
Citation_Abstract_Html_Url = {http://iopscience.iop.org/1367-2630/13/9/095011},
Citation_Authors = {Horsman, Clare},
Citation_Date = {2011-09-01},
Citation_Doi = {10.1088/1367-2630/13/9/095011},
Citation_Firstpage = {095011},
Citation_Journal_Title = {New Journal of Physics},
Citation_Pdf_Url = {http://iopscience.iop.org/1367-2630/13/9/095011/pdf/1367-2630_13_9_095011.pdf},
Citation_Publisher = {IOP Publishing},
Citation_Title = {Quantum picturalism for topological cluster-state computing},
Citation_Volume = {13},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Dc.Contributor = {Horsman, Clare},
Dc.Date = {2011-09-01},
Dc.Description = {IOPscience is a unique platform for IOP-hosted journal content providing site-wide electronic access to more than 130 years of leading scientific research, and incorporates some of the most innovative technologies to enhance your user-experience.},
Dc.Title = {Quantum picturalism for topological cluster-state computing},
Description = {IOPscience is a unique platform for IOP-hosted journal content providing site-wide electronic access to more than 130 years of leading scientific research, and incorporates some of the most innovative technologies to enhance your user-experience.},
Doi = {doi:10.1088/1367-2630/13/9/095011},
Journal = {New J. Phys.},
Keywords = {quantum computing; categorical quantum mechanics},
Month = {September},
Number = {095011},
Robots = {noarchive},
Title = {Quantum picturalism for topological cluster-state computing},
Volume = {13},
Year = {2011},
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Bdsk-Url-1 = {http://dx.doi.org/10.1088/1367-2630/13/9/095011}}
@article{Caulton:2011uq,
Abstract = {Using the Hilbert-Bernays account as a spring-board, we first define four ways in which two objects can be discerned from one another, using the non-logical vocabulary of the language concerned. (These definitions are based on definitions made by Quine and Saunders.) Because of our use of the Hilbert-Bernays account, these definitions are in terms of the syntax of the language. But we also relate our definitions to the idea of permutations on the domain of quantification, and their being symmetries. These relations turn out to be subtle---some natural conjectures about them are false. We will see in particular that the idea of symmetry meshes with a species of indiscernibility that we will call `absolute indiscernibility'. We then report all the logical implications between our four kinds of discernibility. We use these four kinds as a resource for stating four metaphysical theses about identity. Three of these theses articulate two traditional philosophical themes: viz. the principle of the identity of indiscernibles (which will come in two versions), and haecceitism. The fourth is recent. Its most notable feature is that it makes diversity (i.e. non-identity) weaker than what we will call individuality (being an individual): two objects can be distinct but not individuals. For this reason, it has been advocated both for quantum particles and for spacetime points. Finally, we locate this fourth metaphysical thesis in a broader position, which we call structuralism. We conclude with a discussion of the semantics suitable for a structuralist, with particular reference to physical theories as well as elementary model theory.},
Author = {Adam Caulton and Jeremy Butterfield},
Citation_Arxiv_Id = {1106.3862},
Citation_Author = {Butterfield, Jeremy},
Citation_Date = {2011/06/20},
Citation_Online_Date = {2011/06/20},
Citation_Pdf_Url = {http://arxiv.org/pdf/1106.3862},
Citation_Title = {On Kinds of Indiscernibility in Logic and Metaphysics},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1106.3862v1},
Journal = {British Journal for the Philosophy of Science},
Keywords = {logic; philosophy},
Title = {On Kinds of Indiscernibility in Logic and Metaphysics},
Year = {2011},
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@article{Pawlowski:2011qy,
Abstract = {We propose to study `hyperbits' as generalizations of quantum bits: their state spaces are d-dimensional Euclidean balls (d=3 is the Bloch sphere of qubits), while they can be subjected to binary measurements corresponding to any direction in d-dimensional Euclidean space. We show that sending and using one hyperbit from one player to another one is in a certain sense equivalent to sharing arbitrary entanglement and sending 1 classical bit -- at least in the context of certain non-local games. We also demonstrate a fundamental identity for hyperbits, limiting their information processing capabilities. As a consequence, we prove a stronger form of the Information Causality inequality for messages of 1 bit; it encapsulates not only the known information limitations of quantum theory but also complementarity.},
Author = {M. Pawlowski and A. Winter},
Citation_Arxiv_Id = {1106.2409},
Citation_Author = {Winter, A.},
Citation_Date = {2011/06/13},
Citation_Online_Date = {2011/06/13},
Citation_Pdf_Url = {http://arxiv.org/pdf/1106.2409},
Citation_Title = {From Qubits to Hyperbits},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1106.2409},
Keywords = {quantum computing; quantum theory; alternative physical models},
Title = {From Qubits to Hyperbits},
Year = {2011},
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@phdthesis{edwards-thesis-2009,
Abstract = {Interest has grown in recent years in the construction of `quantum-like' theories, toy theories which exhibit some but not all features of quantum mechanics. Such theories are expressed in diverse mathematical terms which may impede comparison of their properties. In this thesis we present a unifying mathematical framework in which we can compare a variety of `quantum-like' theories, based on Abramsky and Coecke's work on applying category theory to quantum mechanics. By doing so we hope to gain a clearer insight into the precise ways in which these theories differ mathematically, and whether this relates to the differences in phenomena which they predict. As an example of this kind of approach, we express Spekkens's toy bit theory within the categorical framework, in the process proving its consistency. The toy bit theory reproduces many features of quantum mechanics, and this is reflected in the fact that within the categorical framework it shares many structural features with quantum mechanics. It differs however, in that it is, by construction, a local hidden variable theory. We develop a categorical treatment of hidden variables, and then demonstrate that the categorical structures which differ between quantum mechanics and the toy theory are exactly those which relate to the question of hidden variables. We extend this to a general result applying to a wider range of theories.},
Author = {Edwards, William},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Keywords = {categorical quantum mechanics; alternative physical models; quantum theory},
School = {Oxford University},
Title = {Non-locality in Categorical Quantum Mechanics},
Year = {2009},
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@article{Barrett:2005lr,
Abstract = {It is well known that measurements performed on spatially separated entangled quantum systems can give rise to correlations that are nonlocal, in the sense that a Bell inequality is violated. They cannot, however, be used for superluminal signaling. It is also known that it is possible to write down sets of ``superquantum'' correlations that are more nonlocal than is allowed by quantum mechanics, yet are still nonsignaling. Viewed as an information-theoretic resource, superquantum correlations are very powerful at reducing the amount of communication needed for distributed computational tasks. An intriguing question is why quantum mechanics does not allow these more powerful correlations. We aim to shed light on the range of quantum possibilities by placing them within a wider context. With this in mind, we investigate the set of correlations that are constrained only by the no-signaling principle. These correlations form a polytope, which contains the quantum correlations as a (proper) subset. We determine the vertices of the no-signaling polytope in the case that two observers each choose from two possible measurements with d outcomes. We then consider how interconversions between different sorts of correlations may be achieved. Finally, we consider some multipartite examples.},
Author = {Jonathan Barrett and Noah Linden and Serge Massar and Stefano Pironio and Sandu Popescu and David Roberts},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevA.71.022101},
Journal = {Phys. Rev. A},
Keywords = {alternative physical models, quantum theory, quantum computing},
Number = {022101},
Title = {Nonlocal correlations as an information-theoretic resource},
Volume = {71},
Year = {2005},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.71.022101}}
@incollection{BobEric2011cats,
Author = {Coecke, Bob and Paquette, Eric Oliver},
Booktitle = {New structures for physics},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Editor = {Coecke, Bob},
Keywords = {category theory},
Pages = {173-286},
Publisher = {Springer},
Series = {Lecture Notes in Physics},
Title = {Categories for the practicing physicist},
Volume = {813},
Year = {2011},
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@article{billbobrob2011,
Author = {Coecke, Bob and Edwards, Bill and Spekkens, R. W.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Journal = {Electronic Notes in Theoretical Computer Science},
Keywords = {categorical quantum mechanics; alternative physical models; quantum theory},
Number = {2},
Pages = {15-36},
Title = {Phase groups and the origin of non-locality for qubits},
Volume = {271},
Year = {2011}}
@inproceedings{Mhalla:2008kx,
Abstract = {Among the models of quantum computation, the One-way Quantum Computer [11,12] is one of the most promising proposals of physical realisation [13], and opens new perspectives for parallelisation by taking advantage of quantum entanglement [2]. Since a One-way QC is based on quantum measurement, which is a fundamentally nondeterministic evolution, a sufficient condition of global determinism has been introduced in [4] as the existence of a causal flow in a graph that underlies the computation. A O(n 3)-algorithm has been introduced [6] for finding such a causal flow when the numbers of output and input vertices in the graph are equal, otherwise no polynomial time algorithm was known for deciding whether a graph has a causal flow or not. Our main contribution is to introduce a O(m)-algorithm for finding a causal flow (where m is the number of edges of the graph), if any, whatever the numbers of input and output vertices are. This answers the open question stated by Danos and Kashefi [4] and by de Beaudrap [6]. Moreover, we prove that our algorithm produces a flow of minimal depth. Whereas the existence of a causal flow is a sufficient condition for determinism, it is not a necessary condition. A weaker version of the causal flow, called gflow (generalised flow) has been introduced in [3] and has been proved to be a necessary and sufficient condition for a family of deterministic computations. Moreover the depth of the quantum computation is upper bounded by the depth of the gflow. However the existence of a polynomial time algorithm that finds a gflow has been stated as an open question in [3]. In this paper we answer this positively with a polynomial time algorithm that outputs an optimal gflow of a given graph and thus finds an optimal correction strategy to the nondeterministic evolution due to measurements.},
Author = {Mehdi Mhalla and Simon Perdrix},
Booktitle = {Automata, Languages and Programming, Proceedings of ICALP 2008},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Description = {Buy academic journals, books and online media at Springer. Choose from thousands of scientific, technology medical and business titles and view our range of services for authors, booksellers and librarians.},
Doi = {10.1007/978-3-540-70575-8_70},
Keywords = {measurement-based quantum computing; quantum computing},
Pages = {857-868},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {Finding Optimal Flows Efficiently},
Volume = {5125},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-540-70575-8_70}}
@inproceedings{Coecke:2010fj,
Abstract = {We present a both simple and comprehensive graphical calculus for quantum computing. We axiomatize the notion of an environment, which together with the axiomatic notion of classical structure enables us to define classical channels, quantum measurements and classical control. If we moreover adjoin the axiomatic notion of complementarity, we obtain sufficient structural power for constructive representation and correctness derivation of typical quantum informatic protocols.},
Author = {Bob Coecke and Simon Perdrix},
Booktitle = {Computer Science Logic},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/978-3-642-15205-4_20},
Editor = {Anuj Dawar and Helmut Veith},
Keywords = {categorical quantum mechanics; graphical calculi; quantum computing},
Pages = {230-244},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {Environment and Classical Channels in Categorical Quantum Mechanics},
Volume = {6247},
Year = {2010},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-15205-4_20}}
@article{Griffiths:1996uq,
Abstract = {It is shown that the Fourier transform preceding the final measurement in Shor's algorithm for factorization on a quantum computer can be carried out in a semiclassical way by using the ``classical'' (macroscopic) signal resulting from measuring one bit to determine the type of measurement carried out on the next bit, and so forth. In this way all the two-bit gates in the Fourier transform can be replaced by a smaller number of one-bit gates controlled by classical signals. This suggests that it may be worthwhile looking for other uses of semiclassical methods in quantum computing.},
Author = {Robert B. Griffiths and Chi-Sheng Niu},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevLett.76.3228},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum computing},
Pages = {3228--3231},
Title = {Semiclassical Fourier Transform for Quantum Computation},
Volume = {76},
Year = {1996},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.76.3228}}
@article{Adriano-Barenco:1995qy,
Abstract = {We show that a set of gates that consists of all one-bit quantum gates [U(2)] and the two-bit exclusive-OR gate [that maps Boolean values (x,y) to (x,x⊕y)] is universal in the sense that all unitary operations on arbitrarily many bits n [U(2n)] can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2) transformation to one input bit if and only if the logical and of all remaining input bits is satisfied. These gates play a central role in many proposed constructions of quantum computational networks. We derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two- and three-bit quantum gates, the asymptotic number required for n-bit Deutsch-Toffoli gates, and make some observations about the number required for arbitrary n-bit unitary operations.},
Author = {Adriano Barenco and Charles H. Bennett and Richard Cleve and David P. DiVincenzo and Norman Margolus and Peter Shor and Tycho Sleator and John A. Smolin and Harald Weinfurter},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevA.52.3457},
Journal = {Phys. Rev. A},
Keywords = {quantum computing},
Pages = {3457--3467},
Title = {Elementary gates for quantum computation},
Volume = {52},
Year = {1995},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.52.3457}}
@inproceedings{Boykin:1999fk,
Abstract = {A novel universal and fault-tolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists of two single-qubit gates (Hadamard and \math), and one double-qubit gate (Controlled-NOT). Since the set consisting of Controlled-NOT and Hadamard gates is not universal, the new basis achieves universality by including only one additional elementary (in the sense that it does not include angles that are irrational multiples of \math) single-qubit gate, and hence, is potentially the simplest universal basis that one can construct. We also provide an alternative proof of universality for the only other known class of universal and fault-tolerant quantum basis.},
Author = {P. Oscar Boykin and Tal Mor and Matthew Pulver and Vwani Roychowdhury and Farrokh Vatan},
Booktitle = {40th Annual Symposium on Foundations of Computer Science},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Dc.Creator = {P. Oscar Boykin, Tal Mor, Matthew Pulver, Vwani Roychowdhury, Farrokh Vatan},
Dc.Date = {1999-10-17},
Dc.Description = {A novel universal and fault-tolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists of two single-qubit gates (Hadamard and \math), and one double-qubit gate (Controlled-NOT). Since the set consisting of Controlled-NOT and Hadamard gates is not universal, the new basis achieves universality by including only one additional elementary (in the sense that it does not include angles that are irrational multiples of \math) single-qubit gate, and hence, is potentially the simplest universal basis that one can construct. We also provide an alternative proof of universality for the only other known class of universal and fault-tolerant quantum basis.},
Dc.Format = {text/html},
Dc.Identifier = {focs},
Dc.Publisher = {Published by the IEEE Computer Society},
Dc.Relation.Ispartof = {focs},
Dc.Title = {On Universal and Fault-Tolerant Quantum Computing: A Novel Basis and a New Constructive Proof of Universality for Shor's Basis},
Dc.Type = {text},
Description = {A novel universal and fault-tolerant basis (set of gates) for quantum computation is described. Such a set is necessary to perform quantum computation in a realistic noisy environment. The new basis consists of two single-qubit gates (Hadamard and \math), and one double-qubit gate (Controlled-NOT). Since the set consisting of Controlled-NOT and Hadamard gates is not universal, the new basis achieves universality by including only one additional elementary (in the sense that it does not include angles that are irrational multiples of \math) single-qubit gate, and hence, is potentially the simplest universal basis that one can construct. We also provide an alternative proof of universality for the only other known class of universal and fault-tolerant quantum basis.},
Doi = {10.1109/SFFCS.1999.814621},
Keywords = {quantum computing},
Pages = {486},
Title = {On Universal and Fault-Tolerant Quantum Computing: A Novel Basis and a New Constructive Proof of Universality for {S}hor's Basis},
Year = {1999},
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Bdsk-Url-1 = {http://dx.doi.org/10.1109/SFFCS.1999.814621}}
@article{DiVincenzo:1995lr,
Abstract = {A proof is given, which relies on the commutator algebra of the unitary Lie groups, that quantum gates operating on just two bits at a time are sufficient to construct a general quantum circuit. The best previous result had shown the universality of three-bit gates, by analogy to the universality of the Toffoli three-bit gate of classical reversible computing. Two-bit quantum gates may be implemented by magnetic resonance operations applied to a pair of electronic or nuclear spins. A ``gearbox quantum computer'' proposed here, based on the principles of atomic-force microscopy, would permit the operation of such two-bit gates in a physical system with very long phase-breaking (i.e., quantum-phase-coherence) times. Simpler versions of the gearbox computer could be used to do experiments on Einstein-Podolsky-Rosen states and related entangled quantum states.},
Author = {David P. DiVincenzo},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1103/PhysRevA.51.1015},
Journal = {Phys. Rev. A},
Keywords = {quantum computing},
Number = {2},
Title = {Two-bit gates are universal for quantum computation},
Url = {http://link.aps.org/doi/10.1103/PhysRevA.51.1015},
Volume = {51},
Year = {1995},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevA.51.1015},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevA.51.1015}}
@inproceedings{Coecke:2010aa,
Abstract = {Multipartite quantum states constitute a (if not the) key resource for quantum computations and protocols. However obtaining a generic, structural understanding of entanglement in N-qubit systems is a long-standing open problem in quantum computer science. Here we show that multipartite quantum entanglement admits a compositional structure, and hence is subject to modern computer science methods. Recall that two N-qubit states are SLOCC-equivalent if they can be inter-converted by stochastic local (quantum) operations and classical communication. There are only two SLOCC-equivalence classes of genuinely entangled 3-qubit states, the GHZ-class and the W-class, and we show that these exactly correspond with two kinds of internal commutative Frobenius algebras on ℂ2 in the symmetric monoidal category of Hilbert spaces and linear maps, namely `special' ones and `anti-special' ones. Within the graphical language of symmetric monoidal categories, the distinction between `special' and `anti-special' is purely topological, in terms of `connected' vs. `disconnected'. These GHZ and W Frobenius algebras form the primitives of a graphical calculus which is expressive enough to generate and reason about representatives of arbitrary N-qubit states. This calculus refines the graphical calculus of complementary observables in [5, ICALP'08], which has already shown itself to have many applications and admit automation. Our result also induces a generalised graph state paradigm for measurement-based quantum computing.},
Author = {Coecke, Bob and Kissinger, Aleks},
Booktitle = {Automata, Languages and Programming, 37th International Colloquium, ICALP 2010, Proceedings Part II},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/978-3-642-14162-1_25},
Editor = {Abramsky, S. and Gavoille, C. and Kirchner, C and Meyer auf der Heide, F. and Spirakis, P. G.},
Eprint = {arXiv:1002.2540},
Keywords = {categorical quantum mechanics, entanglement, graphical calculi, category theory},
Pages = {297-308},
Title = {The Compositional Structure of Multipartite Quantum Entanglement},
Volume = {6199},
Year = {2010},
Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-14162-1_25}}
@article{Lack:2005aa,
Abstract = {We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be examples of adhesive and quasiadhesive categories. Double-pushout graph rewriting generalizes well to rewriting on arbitrary adhesive and quasiadhesive categories.},
Author = {Lack, Stephen and Sobocinski, Pawel},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Description = {RAIRO - Theoretical Informatics and Applications, an international journal on theoretical computer science and its applications},
Doi = {10.1051/ita:2005028},
Generator = {Joomla! 1.5 - Open Source Content Management},
Journal = {Theoretical Informatics and Applications},
Keywords = {category theory, rewriting, graphical calculi},
Number = {3},
Pages = {511 - 545},
Robots = {index, follow, noarchive},
Title = {Adhesive and quasiadhesive categories},
Volume = {39},
Year = {2005},
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Bdsk-Url-1 = {http://dx.doi.org/10.1051/ita:2005028}}
@article{Guiraud:2009aa,
Abstract = {We study convergent (terminating and confluent) presentations of n-categories. Using the notion of polygraph (or computad), we introduce the homotopical property of finite derivation type for n-categories, generalising the one introduced by Squier for word rewriting systems. We characterise this property by using the notion of critical branching. In particular, we define sufficient conditions for an n-category to have finite derivation type. Through examples, we present several techniques based on derivations of 2-categories to study convergent presentations by 3-polygraphs.},
Author = {Guiraud, Yves and Malbos, Philippe},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Journal = {Theory and Applications of Categories},
Keywords = {category theory; rewriting; graphical calculi; polycategories},
Number = {18},
Pages = {420--478},
Title = {Higher-dimensional categories with finite derivation type},
Volume = {22},
Year = {2009},
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@article{Medendorp:2010aa,
Author = {Medendorp, Z. E. D. and Torres-Ruiz, F. A. and Shalm, L. K. and Tabia, G. N. M. and Fuchs, C. A. and Steinberg, A. M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Eprint = {arXiv:1006.4905v1},
Journal = {submitted to PRL},
Keywords = {quantum computing;},
Title = {Experimental characterization of qutrits using SIC-POVMs},
Year = {2010},
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@article{Gore:1998aa,
Author = {Gor{\'e}, Rajeev},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Journal = {Logic Journal of the IGPL},
Keywords = {proof theory; logic},
Number = {3},
Pages = {451-504},
Title = {Substructural Logics On Display},
Volume = {6},
Year = {1998},
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@article{:1998aa,
Abstract = {Many logics in the relevant family can be given a proof theory in the style of Belnap's display logic. However, as originally given, the proof theory is essentially more expressive than the logics they seek to model. In this paper, we consider a modified proof theory which more closely models relevant logics. In addition, we use this proof theory to show decidability for a large range of substructural logics.},
Author = {Restall, Greg},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Journal = {Journal of Philosophical Logic},
Keywords = {proof theory; logic;},
Pages = {179-216},
Title = {Displaying and Deciding Substructural Logics 1: Logics with Contraposition},
Volume = {27},
Year = {1998},
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@article{CarboniStephen-Lack:1993aa,
Abstract = {In recent years, there has been considerable discussion as to the appropriate definition of distributive categories. Three definitions which have had some support are: (1) A category with finite sums and products such that the canonical map δ:A×B+ A×C→A×(B+C) is an isomorphism (Walters). (2) A category with finite sums and products such that the canonical functor +:A/A× A/B→A/(A+B) is an equivalence (Monro). (3) A category with finite sums and finite limits such that the canonical functor + of (2) is an equivalence (Lawvere and Schanuel).There has been some confusion as to which of these was the natural notion to consider. This resulted from the fact that there are actually two elementary notions being combined in the above three definitions. The first, to which we give the name distributivity, is exactly that of (1). The second notion, which we shall call extensivity, is that of a category with finite sums for which the canonical functor + of definitions (2) and (3) is an equivalence. Extensivity, although it implies the existence of certain pullbacks, is essentially a property of having well-behaved sums. It is the existence of these pullbacks which has caused the confusion. The connections between definition (1) and definitions (2) and (3) are that any extensive category with products is distributive in the first sense, and that any category satisfying (3) satisfies (1) locally.The purpose of this paper is to present some basic facts about extensive and distributive categories, and to discuss the relationships between the two notions.},
Author = {Carboni, A. and Lack, S. and Walters, R. F. C.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {doi:10.1016/0022-4049(93)90035-R},
Journal = {Journal of Pure and Applied Algebra},
Keywords = {category theory},
Number = {2},
Pages = {145-158},
Robots = {NOINDEX,NOFOLLOW,NOARCHIVE},
Title = {Introduction to extensive and distributive categories},
Volume = {84},
Year = {1993},
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Bdsk-Url-1 = {http://dx.doi.org/10.1016/0022-4049(93)90035-R}}
@techreport{Lack:2003aa,
Abstract = {We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved. Many types of graphical structures used in computer science are shown to be examples of adhesive categories. Double-pushout graph rewriting generalises well to rewriting on arbitrary adhesive categories.},
Author = {Lack, S. and Sobocinski, P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Institution = {BRICS, Department of Computer Science, University of Aarhus},
Keywords = {category theory; rewriting},
Number = {BRICS RS-03-31},
Title = {Adhesive categories},
Year = {2003},
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@book{Aguiar:2010aa,
Author = {Aguiar, M. and Mahajan, S.},
Booktitle = {Monoidal Functors, Species and Hopf Algebras},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Keywords = {category theory; monoidal categories},
Title = {Monoidal Functors, Species and Hopf Algebras},
Year = {2010},
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@unpublished{Biamonte:2010aa,
Abstract = {It is shown that equations that hold in appropriate monoidal categories have an explicit representation in terms of quantum circuits. Hence, we adjust and map the graphical calculus of Abramsky and Coecke's categorical axiomatization of quantum theory onto quantum circuits, making a suitable extension applicable to problems stated in the language of quantum information science. Viewed in this new way, circuit diagrams themselves now become arrows in a Category, making quantum circuits a special case of a much more general mathematical framework. By building a precise connection between the quantum circuit language and the categorical model, we were able to use this new framework to produce results new to both areas. This should lead to more cross communication between the field of Categorical Quantum Theory, and Quantum Information Science.},
Author = {Biamonte, J. D.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Keywords = {quantum computing; categorical quantum mechanics; rewriting},
Title = {Categorical Models of Quantum Circuits},
Year = {2010},
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@inproceedings{Sobocinski:2010aa,
Abstract = {We introduce a generalisation of open Petri nets, as well as a stateful extension of the calculus of connectors. These two formalisms are shown to have the same expressive power.},
Author = {Sobocinski, P.},
Booktitle = {CONCUR 2010 - Concurrency Theory},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Doi = {10.1007/978-3-642-15375-4_38},
Keywords = {graphical calculi; process algebra; petri-nets},
Pages = {pp 554-568},
Publisher = {Springer},
Series = {LNCS},
Title = {Representations of Petri net interactions},
Volume = {6269},
Year = {2010},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-15375-4_38}}
@misc{Lafont:2010aa,
Abstract = {We give a survey of a diagrammatic syntax for PROs and PROPs,
which are related to the theory of operads and bialgebras. Using diagram rewriting,
we obtain presentations of PROs by generators and relations. In some cases, we even
get convergent rewrite systems. },
Author = {Lafont, Yves},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Howpublished = {Lecture given at the Thematic school : Operads CIRM, Luminy (Marseille), 20-25 April 2009},
Keywords = {operads; graphical calculi; rewriting},
Month = {February},
Title = {Diagram rewriting and operads},
Year = {2010},
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@article{Lamarche:20:aa,
Abstract = {We discuss a general way of defining contexts in linear logic, based on the observation that linear universal algebra can be symmetrized by assigning an additional variable to represent the output of a term. We give two approaches to this, a syntactical one based on a new, reversible notion of term, and an algebraic one based on a simple generalization of typed operads. We relate these to each other and to known examples of logical systems, and show new examples, in particular discussing the relationship between intuitionistic and classical systems. We then present a general framework for extracting deductive systems from a given theory of contexts, and give a generic proof that all these systems have cut-elimination.},
Author = {Lamarche, F.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Journal = {Accepted for publication in Math. Struct. in Comp. Sci},
Keywords = {linear logic; categorical logic; operads;},
Title = {On the Algebra of Structural Contexts},
Year = {2010},
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@unpublished{Edwards:2010aa,
Abstract = {Basis structures (commutative isometric dagger Frobenius comonoids) arise in the categories associated with several quantum-like theories, where they provide the abstract counterparts of orthonormal bases, and are thus associated with the measurement of observables. Every basis structure has a corresponding Abelian group, termed its phase group. Previous work [3] investigated the categories Stab and Spek which correspond respectively to qubit stabiliser quantum mechanics, and the toy bit theory proposed by Rob Spekkens [5]. The two categories exhibit different phase groups, Z4 and Z2 × Z2 respectively. It was shown that this difference exactly underlies the fact that while the predictions of the toy theory can be modelled by local hidden variables, those of the stabiliser theory cannot.
This work attempts to extend this result to more general phase groups. Whilst it does not
succeed in encompassing all possible phase groups, it does extend the result to a large class, many of which might be expected to occur in the categories corresponding to theories of interest. We begin in section 1 by reviewing the key categorical structures which will be used in the paper, and then move on to explicitly characterise which phase groups are covered by the new result, in section 2. Section 3 shows how the issue of local hidden variable theories is treated in the abstract categorical setting. Sections 4 and 5 lay the groundwork for the main result which is described in section 6. This result is essentially a generalisation of Mermin's famous no-go theorem [4] employing the GHZ state. Section 7 makes a link between the main result of the paper and the sub ject of group extensions. Appendix A illustrates the results of the paper using a concrete example. Consideration of this example may aid comprehension of the proof of the general result.
},
Author = {Edwards, Bill},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Keywords = {categorical quantum mechanics; entanglement; alternative physical models; quantum theory},
Month = {June},
Title = {Phase groups and local hidden variables},
Year = {2010},
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@inproceedings{Selinger:2010:aa,
Abstract = {We consider symmetric monoidal categories of convex operational models, and adduce necessary and sufficient conditions for these to be compact-closed or dagger-compact. Compact closure amounts to the condition that all processes be implementable by means of a ``remote evaluation'' protocol (generalizing standard conclusive quantum teleportation protocols), which amounts to a form of classical conditioning. Degenerate dagger compact categories (in which each system is its own dual, not just up to isomorphism, but on the nose) emerge from a further restriction, namely, that a composite of two copies of any systm allowed by the theory admit a symmetric bipartite ``isomorphism'' state.},
Author = {Selinger, P.},
Booktitle = {Proceedings of 7th Workshop on Quantum Physics and Logic (QPL 2010)},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:47 +0000},
Editor = {Coecke, B. and Panangaden, P. and Selinger, P.},
Keywords = {category theory; graphical calculi; monoidal categories},
Title = {Autonomous categories in which ${A} \cong {A}^*$},
Url = {http://www.mscs.dal.ca/~selinger/papers/halftwist-2up.pdf},
Year = {2010},
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@inproceedings{Barnum:2010aa,
Abstract = {We consider symmetric monoidal categories of convex operational models, and adduce necessary and sufficient conditions for these to be compact-closed or dagger-compact. Compact closure amounts to the condition that all processes be implementable by means of a ``remote evaluation'' protocol (generalizing standard conclusive quantum teleportation protocols), which amounts to a form of classical conditioning. Degenerate dagger compact categories (in which each system is its own dual, not just up to isomorphism, but on the nose) emerge from a further restriction, namely, that a composite of two copies of any systm allowed by the theory admit a symmetric bipartite ``isomorphism'' state.},
Author = {Barnum, H. and Duncan, R and Wilce, Alexander},
Booktitle = {Proceedings of 7th Workshop on Quantum Physics and Logic (QPL 2010)},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Coecke, B. and Panangaden, P. and Selinger, P.},
Keywords = {categorical quantum mechanics; alternative physical models},
Title = {Convexity, Categorical Semantics and the Foundations of Physics},
Year = {2010},
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@misc{Arrighi:2010aa,
Abstract = {We provide a rapid introduction to the theory of Cellular Automata (CA), focusing on those results which were influential in the development of Quantum Cellular Automata (QCA). In particular we insist upon the three different ways to define a CA, namely in terms of a local transition rule, a partitioned or block representation, or as a shift-invariant continuous function. We also discuss the influence of the chosen space of configurations upon these presentations. We discuss universal CA. },
Author = {Arrighi, P. and Werner, R. F.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Howpublished = {Lecture notes at the QICS spring school, Oxford, May 2010},
Keywords = {quantum computing; cellular automata; quantum theory},
Month = {May},
Title = {Notes on quantum cellular automata},
Year = {2010},
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@article{Egger:2010aa,
Abstract = {The author has long contended that the notion of symmetric monoidal category
(or even braided monoidal category) is much too strong for the purposes of analysis.
Rather, what is needed is the non-posetal analogue of an involutive quantale [MP92];
that is, a (planar) monoidal category equipped with a covariant involution that reverses
the order of tensoring. In this, our first paper on the sub ject, we study the coherence
issues that inevitably result when passing from posets to categories; we also link our
sub ject with other notions already in the literature, such as balanced braided monoidal
categories [JS91] and dagger pivotal categories [Sel09].
},
Author = {Egger, J. M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {monoidal categories; category theory},
Title = {Involutive monoidal categories},
Year = {2010},
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@article{Wells:1994aa,
Abstract = {This document is an outline of the theory of sketches with pointers to the literature. An extensive bibliography is given. Some coverage is given to related areas such as algebraic theories, categorial model theory and categorial logic as well. An appendix beginning on page 11 provides definitions of some of the less standard terms used in the paper, but the reader is expected to be familiar with the basic ideas of category theory. A rough machine generated index begins on page 21. I would have liked to explain the main ideas of all the papers referred to herein, but I am not familiar enough with some of them to do that. It seemed more useful to be inclusive, even if many papers were mentioned without comment. One consequence of this is that the discussions in this document often go into more detail about the papers published in North America than about those published elsewhere. The DVI file for this article is available by anonymous FTP from ftp.cwru.edu in the directory},
Author = {Wells, Charles},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Description = {CiteSeerX - Document Details (Isaac Councill, Lee Giles): This document is an outline of the theory of sketches with pointers to the literature. An extensive bibliography is given. Some coverage is given to related areas such as algebraic theories, categorial model theory and categorial logic as well. An appendix beginning on page 11 provides definitions of some of the less standard terms used in the paper, but the reader is expected to be familiar with the basic ideas of category theory. A rough machine generated index begins on page 21. I would have liked to explain the main ideas of all the papers referred to herein, but I am not familiar enough with some of them to do that. It seemed more useful to be inclusive, even if many papers were mentioned without comment. One consequence of this is that the discussions in this document often go into more detail about the papers published in North America than about those published elsewhere. The DVI file for this article is available by anonymous FTP from ftp.cwru.edu in the directory},
Keywords = {category theory; sketches},
Title = {Sketches: Outline with References},
Year = {1994},
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@article{Adamek:1995aa,
Abstract = {Every accessible category is proved to be sketchable by a sketch with finite colimits. In contrast, a finitely accessible category is presented that cannot be sketched by a finitary sketch, i.e., a sketch with finite limits and finite colimits. Also, a category sketchable by a finitary sketch is found that is not finitely accessible.},
Author = {Adamek, J. and Rosicky, J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1017/S0960129500000773},
Journal = {Mathematical Structures in Computer Science},
Keywords = {category theory; sketches},
Pages = {315--322},
Title = {Finitary sketches and finitely accessible categories},
Volume = {5},
Year = {1995},
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Bdsk-Url-1 = {http://dx.doi.org/10.1017/S0960129500000773}}
@article{Kraus:2010aa,
Abstract = {The necessary and sufficient conditions for the equivalence of arbitrary n-qubit pure quantum states under Local Unitary (LU) operations derived in [B. Kraus Phys. Rev. Lett. 104, 020504 (2010)] are used to determine the different LU-equivalence classes of up to five-qubit states. Due to this classification new parameters characterizing multipartite entanglement are found and their physical interpretation is given. Moreover, the method is used to derive examples of two n-qubit states (with n>2 arbitrary) which have the properties that all the entropies of any subsystem coincide, however, the states are neither LU-equivalent nor can be mapped into each other by general local operations and classical communication.},
Author = {Kraus, B.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:1005.5295v1},
Keywords = {quantum computing; entanglement},
Title = {Local unitary equivalence and entanglement of multipartite pure states},
Year = {2010},
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@inproceedings{Katis:1997aa,
Abstract = {We have shown that a natural algebraic structure on Span(Graph) allows the compositional specification of concurrent systems. Hoare's parallel operation appears as a derived operation in this algebra. The simpler basic operations of our algebra are possible because we do not insist on interleaving semantics: interleaving prevents consideration of the identity span, as well as other natural constants such as the diagonal. We have given some examples of transforming systems using the equations of the algebra. Associated to the algebra there is a geometry which expresses the distributed nature of a concurrent system. This relation between algebra and geometry makes precise the relation between process algebras and circuit diagrams as used, for example, in Ebergen [E87].},
Author = {Katis, P. and Sabadini, N. and Walters, R. F. C.},
Booktitle = {Algebraic Methodology and Software Technology},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1007/BFb0000479},
Keywords = {categorical logic; graphical calculi; process algebra; rewriting},
Pages = {307-321},
Series = {Lecture Notes in Computer Science},
Title = {Span(Graph): A categorical algebra of transition systems},
Volume = {1349},
Year = {1997},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/BFb0000479}}
@article{Archer:2005aa,
Abstract = {In a quantum system having a finite number N of orthogonal states, two orthonormal bases {ai} and {bj} are called mutually unbiased if all inner products < ai | bj > have the same modulus 1/\sqrt{N}. This concept appears in several quantum information problems. The number of pairwise mutually unbiased bases is at most N + 1 and various constructions of such N + 1 bases have been found when N is a power of a prime number. We study families of formulas that generalize these constructions to arbitrary dimensions using finite rings. We then prove that there exists a set of N + 1 mutually unbiased bases described by such formulas, if and only if N is a power of a prime number.},
Author = {Archer, Claude},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1063/1.1829153},
Eprint = {arXiv:quant-ph/0312204v1},
Journal = {J. Math. Phys},
Keywords = {quantum theory; Mutually unbiased bases; Hilbert spaces},
Number = {022106},
Title = {There is no generalization of known formulas for mutually unbiased bases},
Volume = {46},
Year = {2005},
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Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.1829153}}
@article{Michael-Aschbacher1:2007aa,
Abstract = {Mutually unbiased bases of a Hilbert space can be constructed by partitioning a unitary error basis. We consider this construction when the unitary error basis is a nice error basis. We show that the number of resulting mutually unbiased bases can be at most one plus the smallest prime power contained in the dimension, and therefore that this construction cannot improve upon previous approaches. We prove this by establishing a correspondence between nice mutually unbiased bases and abelian subgroups of the index group of a nice error basis and then bounding the number of such subgroups. This bound also has implications for the construction of certain combinatorial objects called nets.},
Author = {Aschbacher, Michael and Childs, Andrew M. and Wocjan, Pawe{\l}},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1007/s10801-006-0002-y},
Journal = {Journal of Algebraic Combinatorics},
Keywords = {Mutually unbiased bases; quantum computing; quantum theory},
Number = {2},
Pages = {111-123},
Title = {The limitations of nice mutually unbiased bases},
Volume = {25},
Year = {2007},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10801-006-0002-y}}
@article{Wocjan:2005aa,
Author = {Wocjan, P. and Beth, T.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arxiv:quant-ph/0407081},
Journal = {Quantum Information and Computation},
Keywords = {mutually unbiased bases; quantum theory; quantum computing},
Number = {2},
Pages = {093--101},
Title = {New construction of mutually unbiased bases in square dimensions},
Volume = {5},
Year = {2005},
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@inproceedings{Grassl:2004aa,
Abstract = {We provide a partial solution to the problem of constructing mutually unbiased bases (MUBs) and symmetric informationally complete POVMs (SIC-POVMs) in non-prime-power dimensions. An algebraic description of a SIC-POVM in dimension six is given. Furthermore it is shown that several sets of three mutually unbiased bases in dimension six are maximal, i.e., cannot be extended.},
Author = {Grassl, Markus},
Booktitle = {Proceedings ERATO Conference on Quantum Information Science 2004},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0406175},
Keywords = {mutually unbiased bases},
Title = {On SIC-POVMs and MUBs in Dimension 6},
Year = {2004},
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@article{Evans:2009aa,
Abstract = {Finding all the mutually unbiased bases in various dimensions is a problem of fundamental interest in quantum information theory and pure mathematics. The general problem formulated in finite-dimensional Hilbert spaces is open. In the categorical approach to quantum mechanics one can find examples of categories which behave ``like'' the category of finite-dimensional Hilbert spaces in various ways but are subtly different. One such category is the category of sets and relations, $\mathbf{Rel}$. One can formulate the concept of mutually unbiased bases here as well. In this note we classify all the mutually unbiased bases in this category by relating it to a standard question in combinatorics.},
Author = {Evans, Julia and Duncan, Ross and Lang, Alex and Panangaden, Prakash},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.4453},
Keywords = {categorical quantum mechanics; alternative physical models; mutually unbiased bases},
Title = {Classifying all mutually unbiased bases in Rel},
Year = {2009},
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@inproceedings{Duncan:2010aa,
Abstract = {We present a method for verifying measurement-based quantum computations, by producing a quantum circuit equivalent to a given deterministic measurement pattern. We define a diagrammatic presentation of the pattern, and produce a circuit via a rewriting strategy based on the generalised flow of the pattern. Unlike other methods for translating measurement patterns with generalised flow to circuits, this method uses neither ancilla qubits nor acausal loops.},
Author = {Duncan, Ross and Perdrix, Simon},
Booktitle = {Automata, Languages and Programming, 37th International Colloquium, ICALP 2010, Proceedings Part II},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1007/978-3-642-14162-1\_24},
Editor = {Abramsky, S. and Gavoille, C. and Kirchner, C and Meyer auf der Heide, F. and Spirakis, P. G.},
Keywords = {measurement-based quantum computing; quantum computing; graphical calculi; categorical quantum mechanics},
Pages = {285-296},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {Rewriting measurement-based quantum computations with generalised flow},
Volume = {6199},
Year = {2010},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-14162-1_24},
Bdsk-Url-2 = {http://dx.doi.org/10.1007/978-3-642-14162-1%5C_24}}
@techreport{RR-09-04,
Abstract = {We describe a general framework in which we can precisely compare the structures of quantum-like theories which may initially be formulated in quite different mathematical terms. We then use this framework to compare two theories: quantum mechanics restricted to qubit stabiliser states and operations, and a toy theory proposed by Spekkens. We discover that viewed within our framework these theories are very similar, but differ in one key aspect - a four element group we term the phase group which emerges naturally within our framework. In the case of the stabiliser theory this group is Z4 while for Spekkens's theory the group is Z2 x Z2. We further show that the structure of this group is intimately involved in a key physical difference between the theories: whether or not they can be modelled by a local hidden variable theory. This is done by establishing a connection between the phase group, and an abstract notion of GHZ state correlations. We go on to formulate precisely how the stabiliser theory and toy theory are 'similar' by defining a notion of 'mutually unbiased qubit theory', noting that all such theories have four element phase groups. Since Z4 and Z2 xZ2 are the only such groups we conclude that the GHZ correlations in this type of theory can only take two forms, exactly those appearing in the stabiliser theory and those appearing in Spekkens's theory. The results point at a classification of local/non-local behaviours by finite Abelian groups, extending beyond qubits to any finitary theory whose observables are all mutually unbiased.},
Author = {Coecke, Bob and Edwards, Bill and Spekkens, Rob},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Institution = {OUCL},
Keywords = {quantum theory; categorical quantum mechanics; alternative physical models},
Number = {RR-09-04},
Pages = {22},
Title = {The Group Theoretic Origin of Non-Locality For Qubits},
Year = {2009},
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@article{Carbonia:1987aa,
Author = {Carboni, A. and Walters, R.F.C.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {doi:10.1016/0022-4049(87)90121-6},
Journal = {Journal of Pure and Applied Algebra},
Keywords = {category theory; monoidal categories;},
Number = {1-2},
Title = {Cartesian bicategories I},
Volume = {49},
Year = {1987},
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Bdsk-Url-1 = {http://dx.doi.org/10.1016/0022-4049(87)90121-6}}
@article{Carboni:1991aa,
Abstract = {Motivated by the search for a good notion of a ``selfdual'' object in a symmetric monoidal category V, we give an abstract notion of commutative separable algebra in a symmetric monoidal category , such that when V is the category of modules over a commutative ring k we obtain the usual commutative separable algebras. Developing the calculus based on such an abstract notion we are able to prove that the dual category of separable algebras in any compact closed, additive category with coequalizers is in fact a boolean pretopos. We apply this result to give a simple characterization of the categories of continuous representations of profinite groups in discrete finite dimensional k-vector spaces. Finally we show that the same calculus can be applied to symmetric monoidal categories of relations to give an essentially algebraic characterization of such categories.},
Author = {Carboni, Aurelio},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {doi:10.1016/0021-8693(91)90057-F},
Journal = {Journal of Algebra},
Keywords = {algebra, category theory},
Number = {2},
Robots = {NOINDEX,NOFOLLOW,NOARCHIVE},
Title = {Matrices, relations, and group representations},
Volume = {136},
Year = {1991},
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Bdsk-Url-1 = {http://dx.doi.org/10.1016/0021-8693(91)90057-F}}
@misc{quantomatichome,
Author = {Dixon, L. and Duncan, R. and Frot, B. and Kissinger, A. and Merry, A. and Quick, D. and Soloviev, M. and Zamdzhiev, V.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-11-03 11:17:40 +0000},
Keywords = {interactive theorem proving; quantum computing; categorical quantum mechanics; rewriting; graphical calculi},
Note = {https://sites.google.com/site/quantomatic/},
Title = {Quantomatic},
Url = {https://sites.google.com/site/quantomatic/},
Bdsk-Url-1 = {http://dream.inf.ed.ac.uk/projects/quantomatic/},
Bdsk-Url-2 = {https://sites.google.com/site/quantomatic/}}
@article{Coecke:2009aa,
Abstract = {This paper has two tightly intertwined aims: (i) to introduce an intuitive and universal graphical calculus for multi-qubit systems, the ZX-calculus, which greatly simplifies derivations in the area of quantum computation and information. (ii) To axiomatize complementarity of quantum observables within a general framework for physical theories in terms of dagger symmetric monoidal categories. We also axiomatize phase shifts within this framework. Using the well-studied canonical correspondence between graphical calculi and dagger symmetric monoidal categories, our results provide a purely graphical formalisation of complementarity for quantum observables. Each individual observable, represented by a commutative special dagger Frobenius algebra, gives rise to an Abelian group of phase shifts, which we call the phase group. We also identify a strong form of complementarity, satisfied by the Z- and X-spin observables, which yields a scaled variant of a bialgebra.},
Author = {Coecke, Bob and Duncan, Ross},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1088/1367-2630/13/4/043016},
Eprint = {arXiv:0906.4725},
Journal = {New J. Phys},
Keywords = {quantum theory; categorical quantum mechanics; mutually unbiased bases; graphical calculi; monoidal categories; quantum computing},
Number = {043016},
Title = {Interacting Quantum Observables: Categorical Algebra and Diagrammatics},
Url = {http://iopscience.iop.org/1367-2630/13/4/043016/},
Volume = {13},
Year = {2011},
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Bdsk-Url-2 = {http://dx.doi.org/10.1088/1367-2630/13/4/043016}}
@incollection{Selinger:2009aa,
Abstract = {This article is intended as a reference guide to various notions of monoidal categories and their associated string diagrams. It is hoped that this will be useful not just to mathematicians, but also to physicists, computer scientists, and others who use diagrammatic reasoning. We have opted for a somewhat informal treatment of topological notions, and have omitted most proofs. Nevertheless, the exposition is sufficiently detailed to make it clear what is presently known, and to serve as a starting place for more in-depth study. Where possible, we provide pointers to more rigorous treatments in the literature. Where we include results that have only been proved in special cases, we indicate this in the form of caveats.},
Author = {Selinger, Peter},
Booktitle = {New structures for physics},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Coecke, Bob},
Eprint = {arXiv:0908.3347},
Keywords = {graphical calculi; monoidal categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Selinger/A survey of graphical languages for monoidal categories.pdf},
Pages = {289-355},
Publisher = {Springer},
Series = {Lecture Notes in Physics},
Title = {A survey of graphical languages for monoidal categories},
Volume = {813},
Year = {2011},
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@article{Perdrix:2005rw,
Abstract = {Quantum measurement is universal for quantum computation. The model of quantum computation introduced by Nielsen and further developed by Leung relies on a generalized form of teleportation. In order to simulate any n-qubit unitary transformation with this model, 4 auxiliary qubits are required. Moreover Leung exhibited a universal family of observables composed of 4 two-qubit measurements. We introduce a model of quantum computation via measurements only, relying on state transfer: state transfer only retains the part of teleportation which is necessary for computating. In order to simulate any n-qubit unitary transformation with this new model, only one auxiliary qubit is required. Moreover we exhibit a universal family of observables composed of 3 one-qubit measurements and only one two-qubit measurement. This model improves those of Nielsen and Leung in terms of both the number of auxiliary qubits and the number of two-qubit measurements required for quantum universality. In both cases, the minimal amounts of necessary resources are now reached: one auxiliary qubit (because measurement is destructive) and one two-qubit measurement (for creating entanglement).},
Author = {Perdrix, Simon},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0402204v1},
Journal = {International Journal of Quantum Information},
Keywords = {measurement-based quantum computing; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Perdrix/State Transfer instead of Teleportation in Measurement-based.pdf},
Number = {1},
Pages = {219-223},
Title = {State Transfer instead of Teleportation in Measurement-based Quantum Computation},
Volume = {3},
Year = {2005},
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@article{Cabello:2009yf,
Abstract = {We present a Bell-like inequality for testing the Kochen-Specker with locality theorem and the free will theorem. The violation can be observed in actual experiments and would rule out some objections to recent quantum contextuality experiments. Quantum mechanics violates this inequality even though the quantum correlations between the distant systems admit a local description. The violation is due to the correlations between successive compatible measurements on one of the local systems. In this sense, the inequality promotes a quantum contextuality experiment to a quantum nonlocality one and provides a new perspective on quantum nonlocality.},
Author = {Cabello, Adan},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0910.5507},
Keywords = {entanglement; quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Cabello/Proposed Kochen-Specker experiment for quantum nonlocality.pdf},
Title = {Proposed Kochen-Specker experiment for quantum nonlocality},
Year = {2009},
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@phdthesis{Purkeypile:2009sf,
Abstract = {While not yet in commercial existence, quantum computers have the ability to solve certain classes of problems that are not efficiently solvable on existing Turing Machine based (classical) computers. For quantum computers to be of use, methods of programming them must exist. Proposals exist for programming quantum computers, but all of the existing ones suffer from flaws that make them impractical in commercial software development environments. Cove is a framework for programming quantum computers that extends existing classical languages to allow for quantum computation, thus providing a quantum computing toolkit for commercial software developers. Since the target users of Cove are commercial developers, it is an object oriented framework that can be used by multiple languages and also places emphasis on complete documentation. The focus of Cove is not so much on the software product, but on the fundamental concepts that make quantum computing practical for common developers.},
Author = {Purkeypile, Matt},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0911.2423},
Keywords = {quantum computing; programming language},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Purkeypile/Cove A Practical Quantum Computer Programming.pdf},
School = {Colorado Technical University},
Title = {Cove: A Practical Quantum Computer Programming Framework},
Year = {2009},
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@article{McKague:2009hb,
Abstract = {We consider non-local properties of quanternionic quantum mechanics, in which the complex numbers are replaced by the quaternions as the underlying algebra. Specifically, we show that it is possible to construct a non-local box. This allows one to rule out quaternionic quantum mechanics using assumptions about communication complexity or information causality.},
Author = {McKague, Matthew},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0911.1761},
Keywords = {quantum theory; entanglement; alternative physical models},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/McKague/Quaternionic quantum mechanics allows non-local.pdf},
Title = {Quaternionic quantum mechanics allows non-local boxes},
Year = {2009},
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@article{Feldmann:2009jt,
Abstract = {We present a classical probability model appropriate to the description of quantum randomness. This tool, that we have called stochastic gauge system, constitutes a contextual scheme in which the Kolmogorov probability space depends upon the experimental setup, in accordance with quantum mechanics. Therefore, the probability space behaves like a gauge parameter. We discuss the technical issues of this theory and apply the concept to classically emulate quantum entangled states. We exhibit bipartite examples leading to maximum violation of Bell or CHSH inequalities, as well as tripartite cases simulating GHZ or W-states. We address also the question of partially correlated systems and multipartite entanglements. In this model, the classical equivalent of the entanglement entropy is identified with the Kullback-Leibler divergence. Hence, we propose a natural generalisation of this function to multipartite systems, leading to a simple evaluation of the degree of entanglement.},
Author = {Feldmann, Michel},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0911.1525},
Keywords = {quantum theory; alternative physical models;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Feldmann/Classical description of quantum randomness using.pdf},
Title = {Classical description of quantum randomness using stochastic gauge systems},
Year = {2009},
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@article{Nest:2009pi,
Abstract = {Landmark quantum algorithms such as the factoring algorithm achieve exponential gains over the best known classical methods; nevertheless, several of these quantum algorithms are constructed by composing only a small number of elementary operations. How does the concatenation of a few simple blocks result in such an enormous computational power? In this paper we investigate various aspects of this problem. First we formulate general conditions which guarantee that the concatenation of two individually simulatable circuits is efficiently simulatable as well. Applying these criteria, we find that different simulation methods (matrix product states, Clifford operations, matchgates, and others) can be composed with each other while maintaining an overall efficient classical simulation. We then apply these results in the context of quantum algorithms. We show that the performance of Simon's and Shor's algorithms crucially depends on the classical postprocessing of the measurement outcomes. Moreover, it is shown that a recently proposed quantum algorithm, concerned with the estimation of Potts model partition functions, can be simulated efficiently classically. In this paper all simulation results are based on classical sampling techniques.},
Author = {den Nest, M. Van},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0911.1624},
Keywords = {quantum computing; algorithms},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Nest/Classical simulation of quantum algorithms and the role.pdf},
Title = {Classical simulation of quantum algorithms and the role of classical postprocessing},
Year = {2009},
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@article{Deng:2009cs,
Abstract = {We introduce a fresh scheme based on the local hidden variable models to quantify nonlocality for arbitrarily high-dimensional quantum systems. Our scheme explores the minimal amount of white noise that must be added to the system in order to make the system local and realistic. Moreover, the scheme has a clear geometric significance and is numerically computable due to powerful computational and theoretical methods for the class of convex optimization problems known as semidefinite programs.},
Author = {Deng, Dong-Ling and Chen, Jing-Ling and Zhou, Zi-Sui},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.2919},
Keywords = {entanglement; alternative physical models; quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Deng/Quantifying Nonlocality Based on Local Hidden.pdf},
Title = {Quantifying Nonlocality Based on Local Hidden Variable Models},
Year = {2009},
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@article{Pawlowski:2009ph,
Abstract = {Quantum physics exhibits many remarkable features. For example, it gives probabilistic predictions (non-determinism), does not allow copying of unknown states (no-cloning), its correlations are stronger than any classical correlations but information cannot be transmitted faster than light (no-signaling). However, all the mentioned features do not single out quantum physics. A broad class of theories exist which share all of them with quantum mechanics and allow even stronger than quantum correlations. Here, we introduce the principle of Information Causality, stating that communication of m classical bits causes information gain of at most m bits. We show that this principle is respected both in classical and quantum physics, and that all stronger than quantum correlations violate it. We suggest that Information Causality, being a generalization of no-signaling, is one of the foundational properties of Nature.},
Author = {Pawlowski, M. and Paterek, T. and Kaszlikowski, D. and Scarani, V. and Winter, A. and Zukowski, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0905.2292},
Journal = {Nature},
Keywords = {quantum theory; alternative physical models; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Pawlowski/A new physical principle Information Causality.pdf},
Number = {1101},
Title = {A new physical principle: Information Causality},
Volume = {461},
Year = {2009},
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@article{Grabmayer:2009gd,
Abstract = {Some personal recollections on the introduction of `abstract proof systems' as a framework for formulating syntax-independent, general results about rule derivability and admissibility. With a particular eye on the inspiration I owe to Roel de Vrijer: the analogy with abstract rewriting systems.},
Author = {Grabmayer, Clemens},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0911.1412},
Keywords = {proof theory; rewriting},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Grabmayer/From Abstract Rewriting Systems to Abstract.pdf},
Title = {From Abstract Rewriting Systems to Abstract Proof Systems},
Year = {2009},
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@article{Sarvepalli:2009it,
Abstract = {Recently, Ji et al disproved the LU-LC conjecture and showed that the local unitary and local Clifford equivalence classes of the stabilizer states are not always the same. Despite the fact this settles the LU-LC conjecture, a sufficient condition for stabilizer states that violate the LU-LC conjecture is missing. In this paper, we investigate further the properties of stabilizer states with respect to local equivalence. Our first result shows that there exist infinitely many stabilizer states which violate the LU-LC conjecture. In particular, we show that for all numbers of qubits $n\geq 28$, there exist distance two stabilizer states which are counterexamples to the LU-LC conjecture. We prove that for all odd $n\geq 195$, there exist stabilizer states with distance greater than two which are LU equivalent but not LC equivalent. Two important classes of stabilizer states that are of great interest in quantum computation are the cluster states and stabilizer states of the topological quantum codes. Surprisingly, the status of these states with respect to the LU-LC conjecture was not studied. We show that, under some minimal restrictions, both these classes of states preclude any counterexamples. These results have other applications. For instance, they can be used to show that the topological quantum codes do not have any encoded non-Clifford transversal gates. We also prove interesting structural properties of the topological CSS stabilizer states; these results could be of independent interest. We characterize these states in terms of a class of minor closed binary matroids. In addition to making connection with an important open problem in binary matroid theory, this characterization could in some cases could provide an efficient test for CSS states that are not counterexamples.},
Author = {Sarvepalli, Pradeep and Raussendorf, Robert},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0911.1571},
Keywords = {entanglement; quantum many-body; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Sarvepalli/On Local Equivalence, Surface Code States.pdf},
Title = {On Local Equivalence, Surface Code States and Matroids},
Year = {2009},
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@inproceedings{Pavlovic:2009pi,
Abstract = {Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke and Selinger. In particular, we analyze function abstraction in quantum computation, which turns out to characterize its classical interfaces. Some quantum algorithms provide feasible solutions of important hard problems, such as factoring and discrete log (which are the building blocks of modern cryptography). It is of a great practical interest to precisely characterize the computational resources needed to execute such quantum algorithms. There are many ideas how to build a quantum computer. Can we prove some necessary conditions? Categorical semantics help with such questions. We show how to implement an important family of quantum algorithms using just abelian groups and relations.},
Author = {Pavlovic, Dusko},
Booktitle = {Mathematical Foundations of Information Flow},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2016-10-04 13:57:41 +0000},
Doi = {http://dx.doi.org/10.1090/psapm/071},
Edited = {Mon, 09 Nov 2009 16:27:40 GMT},
Editor = {Samson Abramsky and Michael Mislove},
Eprint = {arXiv:1006.1010},
Institution = {OUCL},
Keywords = {category theory, categorical quantum mechanics},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Pavlovic/Geometry of abstraction in quantum computation.pdf},
Organization = {AMS},
Published = {Mon, 09 Nov 2009 16:55:47 GMT},
Series = {Proceedings of Symposia in Applied Mathematics},
Title = {Geometry of abstraction in quantum computation},
Url = {http://www.comlab.ox.ac.uk/publications/publication3347-abstract.html},
Volume = {71},
Year = {2012},
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@article{Mellies:2009p1852,
Author = {Melli{\`e}s, P. A. and Tabareau, N.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Melliès/Free models of T-algebraic theories computed.pdf},
Pmid = {7655745934411679594related:asc_j12sPmoJ},
Rating = {0},
Read = {Yes},
Title = {Free models of T-algebraic theories computed as Kan extensions},
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@inproceedings{Kissinger2009,
Abstract = {Graphical languages provide a powerful tool for describing the behaviour of quantum systems. While the use of graphs vastly reduces the complexity of many calculations, manual graphical manipulation quickly becomes untenable for large graphs or large numbers of graphs. To combat this issue, we are developing a tool called Quantomatic, which allows automated and semi-automated explorations of graph rewrite systems and their underlying semantics. We emphasise in this paper the features of Quantomatic that interact with a computer algebra system to discover graphical relationships via the unification of matrix equations. Since these equations can grow exponentially with the size of the graph, we use this method to discover small identities and use those identities as graph rewrites to expand the theory.},
Author = {Kissinger, Aleks},
Booktitle = {Intelligent Computer Mathematics},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1007/978-3-642-02614-0},
Keywords = {quantum computing; graphical calculi; rewriting},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Kissinger/Exploring a Quantum Theory with Graph.pdf},
Pages = {90-105},
Series = {Lecture Notes in Computer Science},
Title = {Exploring a Quantum Theory with Graph Rewriting and Computer Algebra},
Volume = {5625},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-02614-0}}
@article{S.-Beigi:2009vn,
Abstract = {We show that solely quantum correlations assign outcome probabilities to local quantum measurements in agreement with relativity theory. That is, if the local measurement statistics are quantum mechanical, then the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Conversely, our result shows that if any experiment would give non-local correlations beyond quantum mechanics, quantum theory would be invalidated even locally.},
Author = {S. Beigi and S. Boixo and M. B. Elliott and S. Wehner},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0910.3952},
Keywords = {quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/S. Beigi/Local quantum measurement and relativity imply.pdf},
Title = {Local quantum measurement and relativity imply quantum correlations},
Year = {2009},
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@article{Abramsky:2009yq,
Abstract = {We pursue a model-oriented rather than axiomatic approach to the foundations of Quantum Mechanics, with the idea that new models can often suggest new axioms. This approach has often been fruitful in Logic and Theoretical Computer Science. Rather than seeking to construct a simplified toy model, we aim for a `big toy model', in which both quantum and classical systems can be faithfully represented -- as well as, possibly, more exotic kinds of systems. To this end, we show how Chu spaces can be used to represent physical systems of various kinds. In particular, we show how quantum systems can be represented as Chu spaces over the unit interval in such a way that the Chu morphisms correspond exactly to the physically meaningful symmetries of the systems -- the unitaries and antiunitaries. In this way we obtain a full and faithful functor from the groupoid of Hilbert spaces and their symmetries to Chu spaces. We also consider whether it is possible to use a finite value set rather than the unit interval; we show that three values suffice, while the two standard possibilistic reductions to two values both fail to preserve fullness.},
Author = {Abramsky, Samson},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0910.2393},
Keywords = {categorical quantum mechanics; alternative physical models},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Abramsky/Big Toy Models Representing Physical Systems As Chu Spaces.pdf},
Title = {Big Toy Models: Representing Physical Systems As Chu Spaces},
Year = {2009},
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@article{Abramsky:2009kx,
Abstract = {We revisit our earlier work on the representation of quantum systems as Chu spaces, and investigate the use of coalgebra as an alternative framework. On the one hand, coalgebras allow the dynamics of repeated measurement to be captured, and provide mathematical tools such as final coalgebras, bisimulation and coalgebraic logic. However, the standard coalgebraic framework does not accommodate contravariance, and is too rigid to allow physical symmetries to be represented. We introduce a fibrational structure on coalgebras in which contravariance is represented by indexing. We use this structure to give a universal semantics for quantum systems based on a final coalgebra construction. We characterize equality in this semantics as projective equivalence. We also define an analogous indexed structure for Chu spaces, and use this to obtain a novel categorical description of the category of Chu spaces. We use the indexed structures of Chu spaces and coalgebras over a common base to define a truncation functor from coalgebras to Chu spaces. This truncation functor is used to lift the full and faithful representation of the groupoid of physical symmetries on Hilbert spaces into Chu spaces, obtained in our previous work, to the coalgebraic semantics.},
Author = {Abramsky, Samson},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0910.3959},
Keywords = {categorical quantum mechanics; alternative physical models},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Abramsky/Coalgebras, Chu Spaces, and Representations of Physical Systems.pdf},
Title = {Coalgebras, Chu Spaces, and Representations of Physical Systems},
Year = {2009},
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@article{Drucker:2009bh,
Abstract = {Alongside the development of quantum algorithms and quantum complexity theory in recent years, quantum techniques have also proved instrumental in obtaining results in classical (non-quantum) areas. In this paper we survey these results and the quantum toolbox they use},
Author = {Drucker, Andrew and de Wolf, Ronald},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0910.3376},
Keywords = {quantum computing; complexity},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Drucker/Quantum Proofs for Classical Theorems.pdf},
Title = {Quantum Proofs for Classical Theorems},
Year = {2009},
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@article{Gudder:2009pd,
Abstract = {Although various schemes for anhomomorphic logics for quantum mechanics have been considered in the past we shall mainly concentrate on the quadratic or grade-2 scheme. In this scheme, the grade-2 truth functions are called coevents. We discuss properties of coevents, projections on the space of coevents and the master observable. We show that the set of projections forms an orthomodular poset. We introduce the concept of precluding coevents and show that this is stronger than the previously studied concept of preclusive coevents. Precluding coevents are defined naturally in terms of the master observable. A result that exhibits a duality between preclusive and precluding coevents is given. Some simple examples are presented.},
Author = {Gudder, Stan},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0910.3253},
Keywords = {quantum theory; logic},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Gudder/An anhomomorphic logic for quantum mechanics.pdf},
Title = {An anhomomorphic logic for quantum mechanics},
Year = {2009},
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@article{Iterators:2009qf,
Abstract = {We propose a method for encoding iterators (and recursion operators in general) using interaction nets (INs). There are two main applications for this: the method can be used to obtain a visual nota- tion for functional programs; and it can be used to extend the existing translations of the lambda-calculus into INs to languages with recursive types.},
Author = {Mackie, Ian and Pinto, Jorge Sousa and Vilaca, Miguel},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0910.3321},
Keywords = {graphical calculi; proof-nets; logic},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Iterators/Ian Mackie and Jorge Sousa Pinto and Miguel.pdf},
Title = {Iterators, Recursors and Nets, Interaction},
Year = {2009},
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@article{Revzen:2009ve,
Abstract = {Relative and center of mass cordinates are used to generalize mutually unbiased bases (MUB) and define mutually unbiased bases (MUCB). Maximal entangled states are given as product staes in the collective varibles},
Author = {Revzen, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0910.3035},
Keywords = {mutually unbiased bases; quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Revzen/Maximally Entangled States via Mutual Unbiased.pdf},
Title = {Maximally Entangled States via Mutual Unbiased collective Bases},
Year = {2009},
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@inproceedings{Abramsky:2009gf,
Abstract = {A research programme is set out for developing the use of high-level methods for quantum computation and information, based on the categorical formulation of quantum mechanics introduced by the author and Bob Coecke.},
Author = {Abramsky, Samson},
Booktitle = {Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science: LICS 2004},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0910.3920},
Keywords = {quantum computing; categorical quantum mechanics},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Abramsky/High-Level Methods for Quantum Computation and Information0.pdf},
Pages = {410-414},
Publisher = {IEEE Computer Society},
Title = {High-Level Methods for Quantum Computation and Information},
Year = {2004},
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@article{Menni:2007it,
Abstract = {We prove that the monoidal 2-category of cospans of finite linear orders and surjections is the universal monoidal category with an object X with a semigroup and a cosemigroup structures, where the two structures satisfy a certain 2-dimensional separable algebra condition.},
Author = {Menni, M. and Sabadini, N. and Walters, R. F. C.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0706.1393},
Keywords = {category theory; monoidal categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Menni/A universal property of the monoidal 2-category of cospans.pdf},
Title = {A universal property of the monoidal 2-category of cospans of finite linear orders and surjections},
Year = {2007},
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@article{Raussendorf:2009wd,
Abstract = {We establish a link between contextuality of quantum mechanics and quantum-mechanical computation. Specifically, we show that no deterministic measurement-based quantum computation evaluating a non-linear function can be described by a non-contextual hidden-variable model. We give examples for such computations derived from quantum codes with suitable transversality properties, and from a counterexample to the LU-LC conjecture.},
Author = {Raussendorf, Robert},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0907.5449},
Keywords = {quantum computing; quantum theory; alternative physical models},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Raussendorf/Quantum computation, discreteness, and contextuality.pdf},
Title = {Quantum computation, discreteness, and contextuality},
Year = {2009},
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@article{Jonathan-Allcock:2009pd,
Abstract = {We introduce a fundamental concept -- closed sets of correlations -- for studying non-local correlations. We argue that sets of correlations corresponding to information-theoretic principles, or more generally to consistent physical theories, must be closed under a natural set of operations. Hence, studying the closure of sets of correlations gives insight into which information-theoretic principles are genuinely different, and which are ultimately equivalent. This concept also has implications for understanding why quantum non-locality is limited, and for finding constraints on physical theories beyond quantum mechanics.},
Author = {Allcock, Jonathan and Brunner, Nicolas and Linden, Noah and Popescu, Sandu and Skrzypczyk, Paul and Vertesi, Tamas},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1103/PhysRevA.80.062107},
Eprint = {arXiv:0908.1496},
Journal = {Phys. Rev. A},
Keywords = {quantum theory; alternative physical models; mutually unbiased bases;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Allcock/Closed sets of non-local correlations.pdf},
Number = {062107},
Title = {Closed sets of non-local correlations},
Volume = {80},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.80.062107}}
@article{Lack:2009qf,
Abstract = {Categorical universal algebra can be developed either using Lawvere theories (single-sorted finite product theories) or using monads, and the category of Lawvere theories is equivalent to the category of finitary monads on Set. We show how this equivalence, and the basic results of universal algebra, can be generalized in three ways: replacing Set by another category, working in an enriched setting, and by working with another class of limits than finite products. An important special case involves working with sifted-colimit-preserving monads rather than filtered-colimit-preserving ones.},
Author = {Lack, Stephen and Rosicky, Jiri},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1007/s10485-009-9215-2},
Eprint = {arXiv:0810.2578},
Journal = {Applied Categorical Structures},
Keywords = {category theory; algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Lack/Notions of Lawvere theory.pdf},
Title = {Notions of Lawvere theory},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10485-009-9215-2}}
@article{D.-M.-Appleby:2009ul,
Abstract = {Every quantum state can be represented as a probability distribution over the outcomes of an informationally complete measurement. But not all probability distributions correspond to quantum states. Quantum state space may thus be thought of as a restricted subset of all potentially available probabilities. A recent publication [1] advocates such a representation using symmetric informationally complete (SIC) measurements. Building upon this work we study how this subset--quantum-state space--might be characterized. Our leading characteristic is that the inner products of the probabilities are bounded, a simple condition with nontrivial consequences. To get quantum-state space something more detailed about the extreme points is needed. No definitive characterization is reached, but we see several new interesting features over those in [1], and all in conformity with quantum theory.},
Author = {Appleby, D. M. and Ericsson, Asa and Fuchs, Christopher A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0910.2750},
Keywords = {quantum theory; alternative physical models},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/D. M. Appleby/Properties of QBist State Spaces.pdf},
Title = {Properties of QBist State Spaces},
Year = {2009},
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@incollection{Abramsky:2009zr,
Abstract = {Our aim in this paper is to trace some of the surprising and beautiful connections which are beginning to emerge between a number of apparently disparate topics: Knot Theory, Categorical Quantum Mechanics, and Logic and Computation. We shall focus in particular on the following two topics: - The Temperley-Lieb algebra has always hitherto been presented as a quotient of some sort: either algebraically by generators and relations as in Jones' original presentation, or as a diagram algebra modulo planar isotopy as in Kauffman's presentation. We shall use tools from Geometry of Interaction, a dynamical interpretation of proofs under Cut Elimination developed as an off-shoot of Linear Logic, to give a direct description of the Temperley-Lieb category -- a "fully abstract presentation", in Computer Science terminology. This also brings something new to the Geometry of Interaction, since we are led to develop a planar version of it, and to verify that the interpretation of Cut-Elimination (the "Execution Formula", or "composition by feedback") preserves planarity. - We shall also show how the Temperley-Lieb algebra provides a natural setting in which computation can be performed diagrammatically as geometric simplification -- "yanking lines straight". We shall introduce a "planar lambda-calculus" for this purpose, and show how it can be interpreted in the Temperley-Lieb category.},
Author = {Abramsky, Samson},
Booktitle = {Mathematics of Quantum Computing and Technology},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Chen, G. and Kauffman, L. and Lomonaco, S.},
Eprint = {arXiv:0910.2737},
Keywords = {categorical quantum mechanics; quantum computing; category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Abramsky/Temperley-Lieb Algebra From Knot Theory.pdf},
Pages = {415--458},
Publisher = {Taylor and Francis},
Title = {Temperley-Lieb Algebra: From Knot Theory to Logic and Computation via Quantum Mechanics},
Year = {2008},
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@article{Gavin-K.-Brennen:2009kx,
Abstract = {The one dimensional quantum walk of anyonic systems is presented. The anyonic walker performs braiding operations with stationary anyons of the same type ordered canonically on the line of the walk. Abelian as well as non-Abelian anyons are studied and it is shown that they have very different properties. Abelian anyonic walks demonstrate the expected quadratic quantum speedup. Non-Abelian anyonic walks are much more subtle. The exponential increase of the system's Hilbert space and the particular statistical evolution of non-Abelian anyons give a variety of new behaviors. The position distribution of the walker is related to Jones polynomials, topological invariants of the links created by the anyonic world-lines during the walk. Several examples such as the SU(2) level k and the quantum double models are considered that provide insight to the rich diffusion properties of anyons.},
Author = {Brennen, Gavin K. and Ellinas, Demosthenes and Kendon, Viv and Pachos, Jiannis K. and Tsohantjis, Ioannis and Wang, Zhenghan},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0910.2974},
Keywords = {quantum computing;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Brennen/Anyonic Quantum Walks.pdf},
Title = {Anyonic Quantum Walks},
Year = {2009},
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@article{Wonmin-Son:2009ad,
Abstract = {Bell conjectured that a positive Wigner function does not allow violation of the inequalities imposed by local hidden variable theories. A requirement for this conjecture is ``when phase space measurements are performed.'' We introduce the theory-independent concept of ``operationally local transformations'' which refers to the change of the switch on a local measurement apparatus. We show that two separated parties, performing only phase space measurements on a composite quantum system with a positive Wigner function and performing only operationally local transformations that preserve this positivity, can nonetheless violate Bell's inequality. Such operationally local transformations are realized using entangled ancillae.},
Author = {Son, Wonmin and Kofler, Johannes and Kim, M. S. and Vedral, Vlatko and Brukner, {\v C}aslav},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Description = {Bell conjectured that a positive Wigner function does not allow violation of the inequalities imposed by local hidden variable theories. A requirement for this conjecture is ``when phase space measurements are performed.'' We introduce the theory-independent concept of ``operationally local transformations'' which refers to the change of the switch on a local measurement apparatus. We show that two separated parties, performing only phase space measurements on a composite quantum system with a positive Wigner function and performing only operationally local transformations that preserve this positivity, can nonetheless violate Bell's inequality. Such operationally local transformations are realized using entangled ancillae.},
Doi = {10.1103/PhysRevLett.102.110404},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Son/Positive Phase Space Transformation Incompatible.pdf},
Number = {110404},
Title = {Positive Phase Space Transformation Incompatible with Classical Physics},
Volume = {102},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.102.110404}}
@article{Marcin-Pawowski1:2009vl,
Abstract = {We derive monogamy relations (tradeoffs) between strengths of violations of Bell's inequalities from the nonsignaling condition. Our result applies to general Bell inequalities with an arbitrary large number of partners, outcomes, and measurement settings. The method is simple, efficient, and does not require linear programing. The results are used to derive optimal fidelity for asymmetric cloning in nonsignaling theories.},
Author = {Pawowski, Marcin and Brukner, {\v C}aslav},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Description = {We derive monogamy relations (tradeoffs) between strengths of violations of Bell's inequalities from the nonsignaling condition. Our result applies to general Bell inequalities with an arbitrary large number of partners, outcomes, and measurement settings. The method is simple, efficient, and does not require linear programing. The results are used to derive optimal fidelity for asymmetric cloning in nonsignaling theories.},
Doi = {10.1103/PhysRevLett.102.030403},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum theory; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Pawowski/Monogamy of Bell's Inequality Violations in Nonsignaling.pdf},
Number = {030403},
Title = {Monogamy of Bell's Inequality Violations in Nonsignaling Theories},
Volume = {102},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.102.030403}}
@article{Tomasz-Paterek:2009yf,
Abstract = {Mutually unbiased bases encapsulate the concept of complementarity---the impossibility of simultaneous knowledge of certain observables---in the formalism of quantum theory. Although this concept is at the heart of quantum mechanics, the number of these bases is unknown except for systems of dimension being a power of a prime. We develop the relation between this physical problem and the mathematical problem of finding the number of mutually orthogonal Latin squares. We derive in a simple way all known results about the unbiased bases, find their lower number, and disprove the existence of certain forms of the bases in dimensions different than power of a prime. Using the Latin squares, we construct hidden-variable models which efficiently simulate results of complementary quantum measurements.},
Author = {Paterek, Tomasz and Daki{\'c}, Borivoje and Brukner, {\v C}aslav},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Description = {Mutually unbiased bases encapsulate the concept of complementarity---the impossibility of simultaneous knowledge of certain observables---in the formalism of quantum theory. Although this concept is at the heart of quantum mechanics, the number of these bases is unknown except for systems of dimension being a power of a prime. We develop the relation between this physical problem and the mathematical problem of finding the number of mutually orthogonal Latin squares. We derive in a simple way all known results about the unbiased bases, find their lower number, and disprove the existence of certain forms of the bases in dimensions different than power of a prime. Using the Latin squares, we construct hidden-variable models which efficiently simulate results of complementary quantum measurements.},
Doi = {10.1103/PhysRevA.79.012109},
Journal = {Phys. Rev. A},
Keywords = {mutually unbiased bases; quantum theory; alternative physical models},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Tomasz Paterek/Mutually unbiased bases, orthogonal Latin.pdf},
Number = {012109},
Title = {Mutually unbiased bases, orthogonal Latin squares, and hidden-variable models},
Volume = {79},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.79.012109}}
@article{Briegel:2009sf,
Abstract = {We discuss the possibility of existence of entanglement in biological systems. Our arguments centre on the fact that biological systems are thermodynamic open driven systems far from equilibrium. In such systems error correction can occur which may maintain entanglement despite high levels of de-coherence. We also discuss the possibility of cooling (classical or quantum) at molecular level.},
Author = {Briegel, Hans J. and Popescu, Sandu},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0806.4552},
Keywords = {quantum many-body; biology},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Briegel/Entanglement and intra-molecular cooling in biological systems?.pdf},
Title = {Entanglement and intra-molecular cooling in biological systems? - A quantum thermodynamic perspective},
Year = {2009},
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@article{H.-J.-Briegel:2009hb,
Abstract = {Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics can be harnessed and exploited. A number of models of quantum computation exist, including the now well-studied quantum circuit model. Although these models have been shown to be formally equivalent, their underlying elementary concepts and the requirements for their practical realization can differ significantly. The new paradigm of measurement-based quantum computation, where the processing of quantum information takes place by rounds of simple measurements on qubits prepared in a highly entangled state, is particularly exciting in this regard. In this article we discuss a number of recent developments in measurement-based quantum computation in both fundamental and practical issues, in particular regarding the power of quantum computation, the protection against noise (fault tolerance) and steps toward experimental realization. Moreover, we highlight a number of surprising connections between this field and other branches of physics and mathematics.},
Author = {Briegel, Hans J. and Browne, Dan E. and D{\"u}r, Wolfgang and Raussendorf, Robert and den Nest, Maarten Van},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0910.1116},
Journal = {Nature Physics},
Keywords = {measurement-based quantum computing; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Briegel/Measurement-based quantum computation.pdf},
Number = {1},
Pages = {19-26},
Title = {Measurement-based quantum computation},
Volume = {5},
Year = {2009},
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@article{Wilce:2009jt,
Abstract = {The past decade has seen a remarkable resurgence of the old programme of finding more or less a priori axioms for the mathematical framework of quantum mechanics. The new impetus comes largely from quantum information theory; in contrast to work in the older tradition, which tended to concentrate on structural features of individual quantum systems, the newer work is marked by an emphasis on systems in interaction. Within this newer work, one can discerne two distinct approaches: one is "top-down", and attempts to capture in category-theoretic terms what is distinctive about quantum information processing. The other is "bottom up", attempting to construct non-classical models and theories by hand, as it were, and then characterizing those features that mark out quantum-like behavior. This paper blends these approaches. We present a constructive, bottom-up recipe for building probabilistic theories having strong symmetry properties, using as data any uniform enlargement of the symmetric group $S(E)$ of any set, to a larger group $G(E)$. Subject to some natural conditions, our construction leads to a monoidal category of fully symmetric test spaces, in which the monoidal product is "non-signaling".},
Annote = {presented at QPLVI, Oxford, April 2009},
Author = {Wilce, Alexander},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0910.1527},
Keywords = {alternative physical models; monoidal categories; categorical quantum mechanics},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Wilce/Symmetry and composition in probabilistic theories.pdf},
Title = {Symmetry and composition in probabilistic theories},
Year = {2009},
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@article{Paterek:2009pi,
Abstract = {We offer a piece of evidence that the problems of finding the number of mutually unbiased bases (MUB) and mutually orthogonal Latin squares (MOLS) might not be equivalent. We study a particular procedure which has been shown to relate the two problems and generates complete sets of MUBs in power-of-prime dimensions and three MUBs in dimension six. For these cases, every square from an augmented set of MOLS has a corresponding MUB. We show that this no longer holds for certain composite dimensions.},
Author = {Paterek, T. and Pawlowski, M. and Grassl, M. and Brukner, C.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0910.1439},
Keywords = {quantum theory; mutually unbiased bases; alternative physical models},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Paterek/On the connection between mutually unbiased bases.pdf},
Title = {On the connection between mutually unbiased bases and orthogonal Latin squares},
Year = {2009},
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@article{Zhang:2009cs,
Abstract = {Building on the property that Dirac Notation and operator do not dependent on specific space-time, some basic laws in quantum mechanics under continuous space-time are extended to the discrete case. The notion of probability measure is introduced as we do in usual quantum mechanics and, consequently, the concept of wave function is ruled out naturally. Based solely on $C^\dag$-algebra, which can include any bounded linear Hermitian operators in physics, the dynamical equation on discrete space-time is constructed without involving time and coordinate variables. we find that our approach to dynamics leads directly to the fact that the usual correspondence $\hat{P}\longrightarrow -i\hbar\nabla$ and $\hat{H}\longrightarrow i\hbar\frac{\partial}{\partial t}$ are replaced by $\hat{T}\longrightarrow -i\hbar\delta$, where $\hat{T}$ is the conserved quantity and $\delta$ is the linear derivation. As a result, the momentum and energy operators are excluded from our formalism.},
Author = {Zhang, An-Wei},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0910.1417},
Keywords = {alternative physical models; quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Zhang/Quantum mechanics on Discrete Space-time.pdf},
Title = {Quantum mechanics on Discrete Space-time},
Year = {2009},
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@article{Lecomte:2009ph,
Abstract = {In Logic, non reflexivity translates into the absence of the identity axiom. This opens the field to the treatment of many language phenomena, like fallacies. Ludics, a frame invented by J-Y Girard, because it is founded on loci (adresses) and not on formulae, allows such a treatment.},
Author = {Lecomte, Alain},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0910.1483},
Keywords = {proof theory; linear logic;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Lecomte/Ludique une logique sans axiome d'identité.pdf},
Title = {Ludique : une logique sans axiome d'identit{\'e}},
Year = {2009},
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@article{Mombelli:2009gd,
Abstract = {Exact indecomposable module categories over the tensor category of representations of Hopf algebras that are liftings of quantum linear spaces are classified.},
Author = {Mombelli, Martin},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0907.4517},
Keywords = {monoidal categories; categorical quantum mechanics},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Mombelli/Representations of tensor categories coming from.pdf},
Title = {Representations of tensor categories coming from quantum linear spaces},
Year = {2009},
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@article{G.Sardanashvily:2009kl,
Abstract = {Generalizing differential geometry of smooth vector bundles formulated in algebraic terms of the ring of smooth functions, its derivations and the Koszul connection, one can define differential operators, differential calculus and connections on modules over arbitrary commutative, graded commutative and noncommutative rings. For instance, this is the case of quantum theory, SUSY theory and noncommutative geometry, respectively. The relevant material on this subject is summarized.},
Author = {G.Sardanashvily},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {differential geometry; algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/G.Sardanashvily/Lectures on Differential Geometry of Modules and Rings.pdf},
Title = {Lectures on Differential Geometry of Modules and Rings},
Year = {2009},
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@article{George-Katsirelos:2009ly,
Abstract = {Dealing with large numbers of symmetries is often problematic. One solution is to focus on just symmetries that generate the symmetry group. Whilst there are special cases where breaking just the symmetries in a generating set is complete, there are also cases where no irredundant generating set eliminates all symmetry. However, focusing on just generators improves tractability. We prove that it is polynomial in the size of the generating set to eliminate all symmetric solutions, but NP-hard to prune all symmetric values. Our proof considers row and column symmetry, a common type of symmetry in matrix models where breaking just generator symmetries is very effective. We show that propagating a conjunction of lexicographical ordering constraints on the rows and columns of a matrix of decision variables is NP-hard.},
Author = {Katsirelos, George and Narodytska, Nina and Walsh, Toby},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.5099},
Keywords = {complexity;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/George Katsirelos/Breaking Generator Symmetry.pdf},
Title = {Breaking Generator Symmetry},
Year = {2009},
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@article{Barnum:2009mz,
Abstract = {We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality recently proposed by Pawlowski et. al. (arXiv:0905.2992). We consider two entropic quantities, which we term measurement and mixing entropy. In classical and quantum theory, they are equal, being given by the Shannon and von Neumann entropies respectively; in general, however, they are very different. In particular, while measurement entropy is easily seen to be concave, mixing entropy need not be. In fact, as we show, mixing entropy is not concave whenever the state space is a non-simplicial polytope. Thus, the condition that measurement and mixing entropies coincide is a strong constraint on possible theories. We call theories with this property monoentropic. Measurement entropy is subadditive, but not in general strongly subadditive. Equivalently, if we define the mutual information between two systems A and B by the usual formula I(A:B) = H(A) + H(B) - H(AB) where H denotes the measurement entropy and AB is a non-signaling composite of A and B, then it can happen that I(A:BC) < I(A:B). This is relevant to information causality in the sense of Pawlowski et al.: we show that any monoentropic non-signaling theory in which measurement entropy is strongly subadditive, and also satisfies a version of the Holevo bound, is informationally causal, and on the other hand we observe that Popescu-Rohrlich boxes, which violate information causality, also violate strong subadditivity. We also explore the interplay between measurement and mixing entropy and various natural conditions on theories that arise in quantum axiomatics.},
Author = {Barnum, Howard and Barrett, Jonathan and Clark, Lisa Orloff and Leifer, Matthew and Spekkens, Robert and Stepanik, Nicolas and Wilce, Alex and Wilke, Robin},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.5075},
Keywords = {alternative physical models; quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Barnum/Entropy and Information Causality in General Probabilistic.pdf},
Title = {Entropy and Information Causality in General Probabilistic Theories},
Year = {2009},
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@article{Wang:2009zr,
Abstract = {The theory of quantum error correction was established more than a decade ago as the primary tool for fighting decoherence in quantum information processing. Although great progress has already been made in this field, limited methods are available in constructing new quantum error correction codes from old codes. Here we exhibit a simple and general method to construct new quantum error correction codes by nesting certain quantum codes together. The problem of finding long quantum error correction codes is reduced to that of searching several short length quantum codes with certain properties. Our method works for all length and all distance codes, and is quite efficient to construct optimal or near optimal codes. Two main known methods in constructing new codes from old codes in quantum error-correction theory, the concatenating and pasting, can be understood in the framework of nested quantum error correction codes.},
Author = {Wang, Zhuo and Sun, Kai and Fan, Hen and Vedral, Vlatko},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.5103},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Wang/Nested Quantum Error Correction Codes.pdf},
Title = {Nested Quantum Error Correction Codes},
Year = {2009},
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@article{Badziag:2009ys,
Abstract = {Klyachko and coworkers consider an orthogonality graph in the form of a pentagram, and in this way derive a Kochen-Specker inequality for spin 1 systems. In some low-dimensional situations Hilbert spaces are naturally organised, by a magical choice of basis, into SO(N) orbits. Combining these ideas some very elegant results emerge. We give a careful discussion of the pentagram operator, and then show how the pentagram underlies a number of other quantum "paradoxes", such as that of Hardy.},
Author = {Badziag, Piotr and Bengtsson, Ingemar and Cabello, Adan and Granstrom, Helena and Larsson, Jan-Ake},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.4713},
Keywords = {quantum theory; Hilbert space; algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Badziag/Pentagrams and paradoxes.pdf},
Title = {Pentagrams and paradoxes},
Year = {2009},
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@article{Augusiak:2009rt,
Abstract = {Recently it has been shown that quantum cryptography beyond pure entanglement distillation is possible and a paradigm for the associated protocols has been established. Here we systematically generalize the whole paradigm to the multipartite scenario. We provide constructions of new classes of multipartite bound entangled states, i.e., those with underlying twisted GHZ structure and nonzero distillable cryptographic key. We quantitatively estimate the key from below with help of the privacy squeezing technique.},
Author = {Augusiak, Remigiusz and Horodecki, Pawel},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0811.3603},
Journal = {Phys. Rev. A},
Keywords = {entanglement; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Augusiak/Multipartite secret key distillation and bound entanglement.pdf},
Title = {Multipartite secret key distillation and bound entanglement},
Year = {2009},
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@article{Batanin:2009vn,
Abstract = {One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product. In this paper we continue the work of [7] to adapt the machinery of globular operads [4] to this task. The resulting theory includes the Gray tensor product of 2-categories and the Crans tensor product [12] of Gray categories. Moreover much of the previous work on the globular approach to higher category theory is simplified by our new foundations, and we illustrate this by giving an expedited account of many aspects of Cheng's analysis [11] of Trimble's definition of weak n-category. By way of application we obtain an "Ekmann-Hilton" result for braided monoidal 2-categories, and give the construction of a tensor product of A-infinity algebras.},
Author = {Batanin, Michael and Cisinski, Denis-Charles and Weber, Mark},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.4715},
Keywords = {category theory; algebra; topology},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Batanin/Algebras of higher operads as enriched categories.pdf},
Title = {Algebras of higher operads as enriched categories II},
Year = {2009},
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@article{Weber:2009yq,
Abstract = {One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product of 2-categories. In this paper we continue the developments of [3] and [2] by understanding the natural generalisations of Gray's little brother, the funny tensor product of categories. In fact we exhibit for any higher categorical structure definable by an n-operad in the sense of Batanin [1], an analogous tensor product which forms a symmetric monoidal closed structure on the category of algebras of the operad.},
Author = {Weber, Mark},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.4722},
Keywords = {category theory; algebra; topology},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Weber/Free Products of Higher Operad Algebras.pdf},
Title = {Free Products of Higher Operad Algebras},
Year = {2009},
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@article{Zilber:2009kx,
Abstract = {We carry out a model-theoretic analysis of the Heisenberg algebra. To this end, a geometric structure is associated to the Heisenberg algebra and is shown to be a Zariski geometry. Furthermore, this Zariski geometry is shown to be non-classical, in the sense that it is not interpretable in an algebraically closed field. On assuming self-adjointness of the position and momentum operators, one obtains a discrete substructure of which the original Zariski geometry is seen as the complexification.},
Author = {Zilber, Boris and Solanki, Vinesh},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.4415},
Keywords = {model theory; quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Zilber/Quantum Harmonic Oscillator as a Zariski Geometry.pdf},
Title = {Quantum Harmonic Oscillator as a Zariski Geometry},
Year = {2009},
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@article{Marek-Kus:2009so,
Abstract = {We show that several classes of mixed quantum states in finite-dimensional Hilbert spaces which can be characterized as being, in some respect, 'most classical' can be described and analyzed in a unified way. Among the states we consider are separable states of distinguishable particles, uncorrelated states of indistinguishable fermions and bosons, as well as mixed spin states decomposable into probabilistic mixtures of pure coherent states. The latter were the subject of the recent paper by Giraud et. al., who showed that in the lowest-dimensional, nontrivial case of spin 1, each such state can be decomposed into a mixture of eight pure states. Using our method we prove that in fact four pure states always suffice.},
Author = {Ku{\'s}, Marek and Bengtsson, Ingemar},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0905.0933},
Keywords = {quantum computing; quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Marek Kuś/`Classical' quantum states.pdf},
Title = {`Classical' quantum states},
Year = {2009},
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@article{Selesnick:2007mg,
Abstract = {In modern theories of computation, a significant role is played by the notions of type and typing, and many benefits accrue from careful attention to the ebb and flow of such structures through the course of a computation. We argue here that types are similarly inherent in quantum theory and that benefits may accrue from their careful handling---something that has apparently not been done in physics proper heretofore. In particular, we investigate the type structure of the interaction Lagrangians of the standard model and deduce the chiral symmetry breaking of the weak interaction as a simple and immediate consequence of the careful maintenance of this structure through the course of a possible computation of the appropriate term.},
Author = {Selesnick, S. A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Description = {In modern theories of computation, a significant role is played by the notions of type and typing, and many benefits accrue from careful attention to the ebb and flow of such structures through the course of a computation. We argue here that types are similarly inherent in quantum theory and that benefits may accrue from their careful handling---something that has apparently not been done in physics proper heretofore. In particular, we investigate the type structure of the interaction Lagrangians of the standard model and deduce the chiral symmetry breaking of the weak interaction as a simple and immediate consequence of the careful maintenance of this structure through the course of a possible computation of the appropriate term.},
Doi = {doi:10.1063/1.2747723},
Journal = {J. Math. Phys.},
Keywords = {quantum theory; logic; types},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Selesnick/Type structure and chiral breaking in the standard.pdf},
Number = {072103},
Title = {Type structure and chiral breaking in the standard model},
Volume = {48},
Year = {2007},
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Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.2747723}}
@article{Combescure:2007wk,
Abstract = {In our previous paper \cite{co1} we have shown that the theory of circulant matrices allows to recover the result that there exists $p+1$ Mutually Unbiased Bases in dimension $p$, $p$ being an arbitrary prime number. Two orthonormal bases $\mathcal B, \mathcal B'$ of $\mathbb C^d$ are said mutually unbiased if $\forall b\in \mathcal B, \forall b' \in \mathcal B'$ one has that $$| b\cdot b'| = \frac{1}{\sqrt d}$$ ($b\cdot b'$ hermitian scalar product in $\mathbb C^d$). In this paper we show that the theory of block-circulant matrices with circulant blocks allows to show very simply the known result that if $d=p^n$ ($p$ a prime number, $n$ any integer) there exists $d+1$ mutually Unbiased Bases in $\mathbb C^d$. Our result relies heavily on an idea of Klimov, Munoz, Romero \cite{klimuro}. As a subproduct we recover properties of quadratic Weil sums for $p\ge 3$, which generalizes the fact that in the prime case the quadratic Gauss sums properties follow from our results.},
Author = {Combescure, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1063/1.3078420},
Eprint = {arXiv:0710.5643},
Journal = {Journal of Mathematical Physics},
Keywords = {mutually unbiased bases, algebra, quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Combescure/Block circulant matrices with circulant.pdf},
Number = {032104},
Title = {Block circulant matrices with circulant blocks, weil sums and mutually unbiased bases, II. The prime power case},
Volume = {50},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.3078420}}
@article{Nicolas-C.-Menicucci:2006zi,
Abstract = {We describe a generalization of the cluster-state model of quantum computation to continuous-variable systems, along with a proposal for an optical implementation using squeezed-light sources, linear optics, and homodyne detection. For universal quantum computation, a nonlinear element is required. This can be satisfied by adding to the toolbox any single-mode non-Gaussian measurement, while the initial cluster state itself remains Gaussian. Homodyne detection alone suffices to perform an arbitrary multi-mode Gaussian transformation via the cluster state. We also propose an experiment to demonstrate cluster-based error reduction when implementing Gaussian operations.},
Author = {Menicucci, Nicolas C. and van Loock, Peter and Gu, Mile and Weedbrook, Christian and Ralph, Timothy C. and Nielsen, Michael A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1103/PhysRevLett.97.110501},
Eprint = {arXiv:quant-ph/0605198},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum computing, measurement-based quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Menicucci/Universal Quantum Computation with Continuous-Variable.pdf},
Number = {110501},
Title = {Universal Quantum Computation with Continuous-Variable Cluster States},
Volume = {97},
Year = {2006},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.97.110501}}
@article{Dehornoy:2005ye,
Abstract = {Starting from the observation that Thompson's groups F and V are the geometry groups respectively of associativity, and of associativity together with commutativity, we deduce new presentations of these groups. These presentations naturally lead to introducing a new subgroup of V and a torsion free extension B* of . We prove that and B* are the geometry groups of associativity together with the law x(yz)=y(xz), and of associativity together with a twisted version of this law involving self-distributivity, respectively.},
Author = {Dehornoy, Patrick},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {doi:10.1016/j.jpaa.2005.02.012},
Journal = {Journal of Pure and Applied Algebra},
Keywords = {algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Dehornoy/Geometric presentations for Thompson's groups.pdf},
Pages = {1-44},
Robots = {NOINDEX,NOFOLLOW,NOARCHIVE},
Title = {Geometric presentations for Thompson's groups},
Volume = {203},
Year = {2005},
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Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.jpaa.2005.02.012}}
@inproceedings{Gottesman:1999to,
Abstract = {Since Shor's discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers - the difficulty of describing them on classical computers - also makes it difficult to describe and understand precisely what can be done with them. A formalism describing the evolution of operators rather than states has proven extremely fruitful in understanding an important class of quantum operations. States used in error correction and certain communication protocols can be described by their stabilizer, a group of tensor products of Pauli matrices. Even this simple group structure is sufficient to allow a rich range of quantum effects, although it falls short of the full power of quantum computation.},
Author = {Gottesman, Daniel},
Booktitle = {Proceedings of the XXII International Colloquium on Group Theoretical Methods in Physics},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Corney, S. P. and Delbourgo, R. and Jarvis, P. D.},
Eprint = {arXiv:quant-ph/9807006},
Keywords = {quantum computing;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Gottesman/The Heisenberg Representation of Quantum Computers.pdf},
Pages = {32-43},
Publisher = {International Press},
Title = {The Heisenberg Representation of Quantum Computers},
Year = {1999},
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@article{Selesnick:2003ht,
Abstract = {In this paper we introduce a minimal formal intuitionistic propositional Gentzen sequent calculus for handling quantum types, quantum storage being introduced syntactically along the lines of Girard's of course operator !. The intuitionistic fragment of orthologic is found to be translatable into this calculus by means of a quantum version of the Heyting paradigm. When realized in the category of finite dimensional Hilbert spaces, the familiar qubit arises spontaneously as the irreducible storage capable quantum computational unit, and the necessary involvement of quantum entanglement in the quantum duplication process is plainly and explicitly visible. Quantum computation is modelled by a single extra axiom, and reproduces the standard notion when interpreted in a larger category.},
Author = {Selesnick, S. A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1023/A:1024410829713},
Journal = {International Journal of Theoretical Physics},
Keywords = {quantum computing; logic; linear logic},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Selesnick/Foundation for Quantum Computing.pdf},
Number = {3},
Pages = {383-426},
Title = {Foundation for Quantum Computing},
Volume = {42},
Year = {2003},
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Bdsk-Url-1 = {http://dx.doi.org/10.1023/A:1024410829713}}
@article{L.-de-Francesco-Albasini:2009xi,
Abstract = {We develop further the algebra of cospans and spans of graphs introduced by Katis, Sabadini and Walters for the sequential and parallel composition of processes, adding here data types.},
Author = {{de Francesco Albasini}, L. and Sabadini, N. and Walters, R.F.C.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.4136},
Keywords = {process algebra; category theory; graphical calculi},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/L. de Francesco Albasini/Cospans and spans of graphs: a categorical algebra.pdf},
Title = {Cospans and spans of graphs: a categorical algebra for the sequential and parallel composition of discrete systems},
Year = {2009},
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@article{Shigeru-Yamashita:2009kr,
Abstract = {We perform formal verification of quantum circuits by integrating several techniques specialized to particular classes of circuits. Our verification methodology is based on the new notion of a reversible miter that allows one to leverage existing techniques for circuit simplification of quantum circuits. For reversible circuits which arise as runtime bottlenecks of key quantum algorithms, we develop several verification techniques and empirically compare them. We also combine existing quantum verification tools with the use of SAT-solvers. Experiments with circuits for Shor's number-factoring algorithm, containing thousands of gates, show improvements in efficiency by four orders of magnitude.},
Author = {Yamashita, Shigeru and Markov, Igor},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.4119},
Keywords = {quantum computing;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Yamashita/Fast Equivalence-checking for Quantum Circuits.pdf},
Title = {Fast Equivalence-checking for Quantum Circuits},
Year = {2009},
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@article{Jennings:2009bc,
Abstract = {We consider measurement-based quantum computation using the state of a spin-lattice system in equilibrium with a thermal bath and free to evolve under its own Hamiltonian. Any single qubit measurements disturb the system from equilibrium and, with adaptive measurements performed at a finite rate, the resulting dynamics reduces the fidelity of the computation. We show that it is possible to describe the loss in fidelity by a single quantum operation on the encoded quantum state that is independent of the measurement history. To achieve this simple description, we choose a particular form of spin-boson coupling to describe the interaction with the environment, and perform measurements periodically at a natural rate determined by the energy gap of the system. We found that an optimal cooling exists, which is a trade-off between keeping the system cool enough that the resource state remains close to the ground state, but also isolated enough that the cooling does not strongly interfere with the dynamics of the computation. For a sufficiently low temperature we obtain a fault-tolerant threshold for the couplings to the environment.},
Author = {Jennings, David and Dragan, Andrzej and Barrett, Sean D. and Bartlett, Stephen D. and Rudolph, Terry},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1103/PhysRevA.80.032328},
Eprint = {arXiv:0906.3553},
Journal = {Phys. Rev. A},
Keywords = {measurement-based quantum computing; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Jennings/Quantum computation via measurements on the low-temperature state.pdf},
Number = {032328},
Title = {Quantum computation via measurements on the low-temperature state of a many-body system},
Volume = {80},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.80.032328}}
@incollection{Abramsky:2009fx,
Author = {Abramsky, Samson and Tzevelekos, Nikos},
Booktitle = {New structures for physics},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {B. Coecke},
Keywords = {categorical logic; monoidal categories; proof theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Abramsky/Introduction to Categories and Categorical Logic.pdf},
Pages = {3--94},
Publisher = {Springer},
Series = {Lecture Notes in Physics},
Title = {Introduction to Categories and Categorical Logic},
Volume = {813},
Year = {2011},
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@article{Quantum-Computing-II:2007os,
Abstract = {In this continuation of an earlier paper we develop further the theme of quantum logical specification and derive from it some apparently physically viable instantiations of potential quantum computing devices. Specifically, in the case of a one-parameter set of terms (or labels)---read as instants of time---we find, emerging quite naturally from the algebraic setup, the paradigm for a single qubit epitomized by the case of a two-state fermion interacting with an external single mode boson. This covers the cases: cavity QED, trapped ions, and, when the qubits are multiplexed appropriately, NMR based systems. (This case degenerates to one in which only bosons are relevant as in the case of pure bosonic harmonic oscillator models in the ``dual rail'' representation. Such models fly in the face of the logic itself, thus clearly revealing even at this level their well-known shortcomings as practical quantum computing devices. Here as elsewhere logical constraints apparently dominate physical ones.) In a final section we indicate briefly how this process exactly generalizes, in the case of a manifold of terms more general than the one-parameter case, to yield the notion of holonomic quantum computation. In the course of this investigation we find an interpretation of path integrals as limits of sequences of logical CUTS, thus establishing a link---though still tenuous---between ensembles of acts of quantum computation and Lagrangians.},
Author = {Selesnick, S. A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1007/s10773-006-9254-5},
Journal = {International Journal of Theoretical Physics},
Keywords = {quantum computing; quantum theory; logic},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Selesnick/Foundation for Quantum Computing II.pdf},
Number = {4},
Pages = {984-1002},
Title = {Foundation for Quantum Computing II},
Volume = {46},
Year = {2007},
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@book{Selesnick:1998tw,
Author = {Selesnick, Stephen A.},
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Keywords = {quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Selesnick/Quanta, Logic and Spacetime.pdf},
Publisher = {World Scientific},
Title = {Quanta, Logic and Spacetime},
Year = {1998},
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@inproceedings{R.-Cleve:2000jw,
Abstract = {We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n+log log(1//spl epsiv/)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2/sup n/ with error bounded by /spl epsiv/. Thus, even for exponentially small error, our circuits have depth O(log n). The best previous depth bound was O(n), even for approximations with constant error. Moreover, our circuits have size O(n log(n//spl epsiv/)). As an application of this depth bound, we show that P. Shor's (1997) factoring algorithm may be based on quantum circuits with depth only O(log n) and polynomial size, in combination with classical polynomial-time pre- and postprocessing. Next, we prove an /spl Omega/(log n) lower bound on the depth complexity of approximations of the QFT with constant error. This implies that the above upper bound is asymptotically tight (for a reasonable range of values of /spl epsiv/). We also give an upper bound of O(n(log n)/sup 2/ log log n) on the circuit size of the exact QFT modulo 2/sup n/, for which the best previous bound was O(n/sup 2/). Finally, based on our circuits for the QFT with power-of-2 moduli, we show that the QFT with respect to an arbitrary modulus m can be approximated with accuracy /spl epsiv/ with circuits of depth O((log log m)(log log 1//spl epsiv/)) and size polynomial in log m+log(1//spl epsiv/).},
Author = {Cleve, R. and Watrous, J.},
Booktitle = {41st Annual Symposium on Foundations of Computer Science},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Dc.Creator = {R. Cleve, J. Watrous},
Dc.Date = {2000-11-12},
Dc.Description = {We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n+log log(1//spl epsiv/)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2/sup n/ with error bounded by /spl epsiv/. Thus, even for exponentially small error, our circuits have depth O(log n). The best previous depth bound was O(n), even for approximations with constant error. Moreover, our circuits have size O(n log(n//spl epsiv/)). As an application of this depth bound, we show that P. Shor's (1997) factoring algorithm may be based on quantum circuits with depth only O(log n) and polynomial size, in combination with classical polynomial-time pre- and postprocessing. Next, we prove an /spl Omega/(log n) lower bound on the depth complexity of approximations of the QFT with constant error. This implies that the above upper bound is asymptotically tight (for a reasonable range of values of /spl epsiv/). We also give an upper bound of O(n(log n)/sup 2/ log log n) on the circuit size of the exact QFT modulo 2/sup n/, for which the best previous bound was O(n/sup 2/). Finally, based on our circuits for the QFT with power-of-2 moduli, we show that the QFT with respect to an arbitrary modulus m can be approximated with accuracy /spl epsiv/ with circuits of depth O((log log m)(log log 1//spl epsiv/)) and size polynomial in log m+log(1//spl epsiv/).},
Dc.Format = {text/html},
Dc.Identifier = {10.1109/SFCS.2000.892140},
Dc.Publisher = {Published by the IEEE Computer Society},
Dc.Relation.Ispartof = {focs},
Dc.Title = {Fast parallel circuits for the quantum Fourier transform},
Dc.Type = {text},
Description = {We give new bounds on the circuit complexity of the quantum Fourier transform (QFT). We give an upper bound of O(log n+log log(1//spl epsiv/)) on the circuit depth for computing an approximation of the QFT with respect to the modulus 2/sup n/ with error bounded by /spl epsiv/. Thus, even for exponentially small error, our circuits have depth O(log n). The best previous depth bound was O(n), even for approximations with constant error. Moreover, our circuits have size O(n log(n//spl epsiv/)). As an application of this depth bound, we show that P. Shor's (1997) factoring algorithm may be based on quantum circuits with depth only O(log n) and polynomial size, in combination with classical polynomial-time pre- and postprocessing. Next, we prove an /spl Omega/(log n) lower bound on the depth complexity of approximations of the QFT with constant error. This implies that the above upper bound is asymptotically tight (for a reasonable range of values of /spl epsiv/). We also give an upper bound of O(n(log n)/sup 2/ log log n) on the circuit size of the exact QFT modulo 2/sup n/, for which the best previous bound was O(n/sup 2/). Finally, based on our circuits for the QFT with power-of-2 moduli, we show that the QFT with respect to an arbitrary modulus m can be approximated with accuracy /spl epsiv/ with circuits of depth O((log log m)(log log 1//spl epsiv/)) and size polynomial in log m+log(1//spl epsiv/).},
Doi = {10.1109/SFCS.2000.892140},
Howpublished = {Fast parallel circuits for the quantum Fourier transform},
Keywords = {complexity; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Cleve/Fast parallel circuits for the quantum Fourier.ps},
Pages = {526},
Publisher = {IEEE Computer Society},
Title = {Fast parallel circuits for the quantum Fourier transform},
Year = {2000},
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Bdsk-Url-1 = {http://dx.doi.org/10.1109/SFCS.2000.892140}}
@incollection{Jozsa:2005qa,
Abstract = {In the formalism of measurement based quantum computation we start with a given fixed entangled state of many qubits and perform computation by applying a sequence of measurements to designated qubits in designated bases. The choice of basis for later measurements may depend on earlier measurement outcomes and the final result of the computation is determined from the classical data of all the measurement outcomes. This is in contrast to the more familiar gate array model in which computational steps are unitary operations, developing a large entangled state prior to some final measurements for the output. Two principal schemes of measurement based computation are teleportation quantum computation (TQC) and the so-called cluster model or one-way quantum computer (1WQC). We will describe these schemes and show how they are able to perform universal quantum computation. We will outline various possible relationships between the models which serve to clarify their workings. We will also discuss possible novel computational benefits of the measurement based models compared to the gate array model, especially issues of parallelisability of algorithms.},
Author = {Jozsa, Richard},
Booktitle = {Quantum information processing: from theory to experiment},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Angelakis, Dimitris G. and Christiandl, Matthias and Ekert, Artur and Kay, Alastair and Kulik, Sergei},
Eprint = {arXiv:quant-ph/0508124},
Keywords = {measurement-based quantum computing; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Jozsa/An introduction to measurement based quantum computation.pdf},
Pages = {137--158},
Publisher = {IOS Press},
Title = {An introduction to measurement based quantum computation},
Year = {2006},
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@article{Hooft:2009yf,
Abstract = {In an attempt to re-establish space-time as an essential frame for formulating quantum gravity - rather than an "emergent" one -, we find that exact invariance under scale transformations is an essential new ingredient for such a theory. Use is made of the principle of "black hole complementarity", the notion that observers entering a black hole describe its dynamics in a way that appears to be fundamentally different from the description by an outside observer. These differences can be boiled down to conformal transformations. If we add these to our set of symmetry transformations, black holes, space-time singularities, and horizons disappear, while causality and locality may survive as important principles for quantum gravity.},
Author = {{'t Hooft}, Gerard},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.3426},
Keywords = {quantum gravity; relativity},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/'t Hooft/Quantum gravity without space-time singularities.pdf},
Title = {Quantum gravity without space-time singularities or horizons},
Year = {2009},
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@article{Montanaro:2009ph,
Abstract = {An XOR function is a function of the form g(x,y) = f(x + y), for some boolean function f on n bits. We study the quantum and classical communication complexity of XOR functions. In the case of exact protocols, we show that, when f is monotone, g's quantum and classical complexities are quadratically related, and that when f is a linear threshold function, g's quantum complexity is Theta(n). More generally, we make a structural conjecture about the Fourier spectra of boolean functions which, if true, would imply that the quantum and classical deterministic communication complexities of all XOR functions are asymptotically equivalent. We give two randomised classical protocols for general XOR functions which are efficient for certain functions, and a third protocol for linear threshold functions with high margin. These protocols operate in the symmetric message passing model with shared randomness.},
Author = {Montanaro, Ashley and Osborne, Tobias},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.3392},
Keywords = {quantum computing, complexity},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Montanaro/On the communication complexity of XOR functions.pdf},
Title = {On the communication complexity of XOR functions},
Year = {2009},
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@article{:2003eu,
Abstract = {We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of a (2n+1)×(2n+1) binary matrix product and binary quadratic forms. As an application we give two schemes to efficiently decompose Clifford group operations into one- and two-qubit operations. We also show how the coefficients of stabilizer states and Clifford group operations in a standard basis expansion can be described by binary quadratic forms. Our results are useful for quantum error correction, entanglement distillation, and possibly quantum computing.},
Author = {Dehaene, Jeroen and Moor, Bart De},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1103/PhysRevA.68.042318},
Eprint = {http://link.aps.org/doi/10.1103/PhysRevA.68.042318},
Journal = {Phys. Rev. A},
Keywords = {quantum computing; measurement-based quantum computing; algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Dehaene/Clifford group, stabilizer states, and linear.pdf},
Number = {042318},
Title = {Clifford group, stabilizer states, and linear and quadratic operations over GF(2)},
Volume = {68},
Year = {2003},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.68.042318}}
@article{Lloyd:1999nx,
Abstract = {This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field might be constructed using simple linear devices such as beam splitters and phase shifters, together with squeezers and nonlinear devices such as Kerr-effect fibers and atoms in optical cavities. Such a device could in principle perform ``quantum floating point'' computations. Problems involving noise, finite precision, and error correction are discussed.},
Author = {Lloyd, Seth and Braunstein, Samuel L.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1103/PhysRevLett.82.1784},
Eprint = {http://link.aps.org/doi/10.1103/PhysRevLett.82.1784},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Lloyd/Quantum Computation over Continuous Variables.pdf},
Number = {8},
Pages = {1784 - 1787},
Title = {Quantum Computation over Continuous Variables},
Volume = {82},
Year = {1999},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.82.1784}}
@article{Day:2006wd,
Abstract = {We give a list of examples of $*$-autonomous structures occurring in mathematical quantum theory.},
Author = {Day, Brian J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:math/0605037},
Keywords = {category theory; monoidal categories; quantum theory; categorical quantum mechanics},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Day/$*$-Autonomous categories in quantum theory.pdf},
Title = {$*$-Autonomous categories in quantum theory},
Year = {2006},
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@article{M.-Goze:2009cr,
Abstract = {We construct an universal enveloping algebra associated to the ternary extension of Lie (super)algebras called Lie algebra of order three. A Poincar\'e-Birkhoff-Witt theorem is proven is this context. It this then shown that this universal enveloping algebra can be endowed with a structure of Hopf algebra. The study of the dual of the universal enveloping algebra enables to define the parameters of the transformation of a Lie algebra of order three. It turns out that these variables are the variables which generate the three-exterior algebra.},
Author = {Goze, M. and {Rausch de Traubenberg}, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0809.4212},
Journal = {J. Math. Phys.},
Keywords = {algebra; category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Goze/Hopf algebras for ternary algebras.pdf},
Number = {063508},
Title = {Hopf algebras for ternary algebras},
Volume = {50},
Year = {2009},
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@article{Stephen-Brierley:2009rr,
Abstract = {All complex Hadamard matrices in dimensions two to five are known. We use this fact to derive all inequivalent sets of mutually unbiased (MU) bases in low dimensions. We find a three-parameter family of triples of MU bases in dimension four and two inequivalent classes of MU triples in dimension five. We confirm that the complete sets of (d+1) MU bases are unique (up to equivalence) in dimensions below six, using only elementary arguments for d less than five.},
Author = {Brierley, Stephen and Weigert, Stefan and Bengtsson, Ingemar},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0907.4097},
Keywords = {mutually unbiased bases},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Brierley/All Mutually Unbiased Bases in Dimensions Two to Five.pdf},
Title = {All Mutually Unbiased Bases in Dimensions Two to Five},
Year = {2009},
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@article{Day:2006dq,
Abstract = {This article represents a preliminary attempt to link Kan extensions, and some of their further developments, to Fourier theory and quantum algebra through *-autonomous monoidal categories and related structures.},
Author = {Day, Brian J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory; quantum theory; graphical calculi},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Day/Monoidal functor categories and graphic Fourier.pdf},
Title = {Monoidal functor categories and graphic Fourier transforms},
Year = {2006},
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@article{Combescure:2007lq,
Abstract = {In this paper, we consider the problem of Mutually Unbiased Bases in prime dimension $d$. It is known to provide exactly $d+1$ mutually unbiased bases. We revisit this problem using a class of circulant $d \times d$ matrices. The constructive proof of a set of $d+1$ mutually unbiased bases follows, together with a set of properties of Gauss sums, and of bi-unimodular sequences.},
Author = {Combescure, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {mutually unbiased bases},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Combescure/Circulant matrices, gauss sums and mutually.pdf},
Title = {Circulant matrices, gauss sums and mutually unbiased I. The prime number case},
Year = {2007},
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@article{Chris-Heunen:2009bh,
Abstract = {This paper investigates quantum logic from the perspective of categorical logic, and starts from minimal assumptions, namely the existence of involutions/daggers and kernels. The resulting structures turn out to (1) encompass many examples of interest, such as categories of relations, partial injections, Hilbert spaces (also modulo phase), and Boolean algebras, and (2) have interesting categorical/logical properties, in terms of kernel fibrations, such as existence of pullbacks, factorisation, and orthomodularity. For instance, the Sasaki hook and and-then connectives are obtained, as adjoints, via the existential-pullback adjunction between fibres.},
Author = {Heunen, Chris and Jacobs, Bart},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0902.2355v2},
Keywords = {quantum theory; categorical logic; categorical quantum mechanics},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Chris Heunen/Quantum Logic in Dagger Kernel Categories.pdf},
Title = {Quantum Logic in Dagger Kernel Categories},
Year = {2009},
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@article{A.-H.-Werner:2009pd,
Abstract = {We propose a quantum key distribution protocol based on a quantum retrodiction protocol, known as the Mean King problem. The protocol uses a two way quantum channel. We show security against coherent attacks in a transmission error free scenario, even if Eve is allowed to attack both transmissions. This establishes a connection between retrodiction and key distribution.},
Author = {Werner, A. H. and Franz, T. and Werner, R. F.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.3375},
Keywords = {quantum computing;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Werner/Quantum cryptography as a retrodiction problem.pdf},
Title = {Quantum cryptography as a retrodiction problem},
Year = {2009},
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@article{Gross:2009qf,
Abstract = {We establish novel methods for quantum state and process tomography based on compressed sensing. Our protocols require only simple Pauli measurements, and use fast classical post-processing based on convex optimization. Using these techniques, it is possible to reconstruct an unknown density matrix of rank r using O(r d log^2 d) measurement settings, a significant improvement over standard methods that require d^2 settings. The protocols are stable against noise, and extend to states which are approximately low-rank. The acquired data can be used to certify that the state is indeed close to a low-rank one, so no a priori assumptions are needed. We present both theoretical bounds and numerical simulations.},
Author = {Gross, David and Liu, Yi-Kai and Flammia, Steven T. and Becker, Stephen and Eisert, Jens},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.3304},
Keywords = {quantum theory; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Gross/Quantum state tomography via compressed sensing.pdf},
Title = {Quantum state tomography via compressed sensing},
Year = {2009},
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@incollection{Heunen:2009ul,
Abstract = {New foundations for quantum logic and quantum spaces are constructed by merging algebraic quantum theory and topos theory. Interpreting Bohr's "doctrine of classical concepts" mathematically, given a quantum theory described by a noncommutative C*-algebra A, we construct a topos T(A), which contains the "Bohrification" B of A as an internal commutative C*-algebra. Then B has a spectrum, a locale internal to T(A), the external description S(A) of which we interpret as the "Bohrified" phase space of the physical system. As in classical physics, the open subsets of S(A) correspond to (atomic) propositions, so that the "Bohrified" quantum logic of A is given by the Heyting algebra structure of S(A). The key difference between this logic and its classical counterpart is that the former does not satisfy the law of the excluded middle, and hence is intuitionistic. When A contains sufficiently many projections (e.g. when A is a von Neumann algebra, or, more generally, a Rickart C*-algebra), the intuitionistic quantum logic S(A) of A may also be compared with the traditional quantum logic, i.e. the orthomodular lattice of projections in A. This time, the main difference is that the former is distributive (even when A is noncommutative), while the latter is not. This chapter is a streamlined synthesis of 0709.4364, 0902.3201, 0905.2275.},
Author = {Heunen, Chris and Landsman, Nicolaas P. and Spitters, Bas},
Booktitle = {Deep Beauty},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Halvorson, H.},
Eprint = {arXiv:0909.3468},
Keywords = {quantum theory; categorical quantum mechanics; toposes},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Heunen/Bohrification.pdf},
Title = {Bohrification},
Year = {2009},
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@article{Barrett:2009zr,
Abstract = {We show that the usefulness of the thermal state of a specific spin-lattice model for measurement-based quantum computing exhibits a transition between two distinct "phases" -- one in which every state is a universal resource for quantum computation, and another in which any local measurement sequence can be simulated efficiently on a classical computer. Remarkably, this transition in computational power does not coincide with any phase transition, classical or quantum, in the underlying spin-lattice model.},
Author = {Barrett, Sean D. and Bartlett, Stephen D. and Doherty, Andrew C. and Jennings, David and Rudolph, Terry},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0807.4797},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Barrett/Transitions in the computational power of thermal states.pdf},
Title = {Transitions in the computational power of thermal states for measurement-based quantum computation},
Year = {2009},
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@inproceedings{Bering:2009ij,
Abstract = {We look at two examples of homotopy Lie algebras (also known as L_{\infty} algebras) in detail from two points of view. We will exhibit the algebraic point of view in which the generalized Jacobi expressions are verified by using degree arguments and combinatorics. A second approach using the nilpotency of Grassmann-odd differential operators \Delta to verify the homotopy Lie data is shown to produce the same results.},
Author = {Bering, Klaus and Lada, Tom},
Booktitle = {Proceedings of the 29th Srni winter school "Geometry and Physics"},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0903.5433},
Keywords = {algebra, topology},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Bering/Examples of Homotopy Lie Algebras.pdf},
Title = {Examples of Homotopy Lie Algebras},
Year = {2009},
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@article{E.:2009sp,
Abstract = {A one way partial quantum bit commitment protocol is developed, using states with built-in classical correlation, completely independent of entanglement. It involves concealing information in a set of mutually non-orthogonal states and revealing it through measurements on a set of product states that are mutually orthogonal. Given $2^N$ choices to commit from, the protocol encodes each choice in a $N+1$ qubit state, from $2^N$ non-orthogonal states. A previously agreed upon $N$ qubit state corresponding to each choice, when coupled with the $N+1$ qubit state, yields an element belonging to a set of orthogonal product states, which can be deterministically distinguished. The protocol is demonstrated by implementing it for a `coin-toss' game. A procedure to enhance security of the protocol is explicated, increasing the number of qubits required. Thus a modification is suggested to reduce this required number.},
Author = {Prasath, E. Sriram and Panigrahi, Prasanta K.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.3117},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/E./One way quantum bit commitment through classical correlation.pdf},
Title = {One way quantum bit commitment through classical correlation},
Year = {2009},
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@article{Wada:2009hc,
Abstract = {We argue that quantum mechanics makes sense without such controversial postulates as the wave function collapse, the quantum probability rule and the observable postulate. We only need the existence of a wave function as a representation of a state, its dynamical evolution rule and another rather trivial postulate proposed here (Read-Off Postulate). The wave function collapse and the probability rule are replaced with intrinsic properties of the theory, i.e. decoherence and relative frequency, respectively. Interpretation of the wave function as a faithful representation of the reality naturally emerges, although quantum reality has a peculiar feature which distinguishes it from classical reality.},
Author = {Wada, Sumio},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.3188},
Keywords = {quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Wada/Minimal Set of Quantum Postulates and Realistic Interpretation.pdf},
Title = {Minimal Set of Quantum Postulates and Realistic Interpretation of Quantum Mechanics},
Year = {2009},
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@article{Alfsen:2009dp,
Abstract = {Let S_k be the set of separable states on B(C^m \otimes C^n) admitting a representation as a convex combination of k pure product states, or fewer. If m>1, n> 1, and k \le max(m,n), we show that S_k admits a subset V_k such that V_k is dense and open in S_k, and such that each state in V_k has a unique decomposition as a convex combination of pure product states, and we describe all possible convex decompositions for a set of separable states that properly contains V_k. In both cases we describe the associated faces of the space of separable states, which in the first case are simplexes, and in the second case are direct convex sums of faces that are isomorphic to state spaces of full matrix algebras. As an application of these results, we characterize all affine automorphisms of the convex set of separable states, and all automorphisms of the state space of B(C^m otimes C^n). that preserve entanglement and separability.},
Author = {Alfsen, Erik and Shultz, Fred},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0906.1761},
Keywords = {quantum theory, entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Alfsen/Unique decompositions, faces, and automorphisms of separable.pdf},
Title = {Unique decompositions, faces, and automorphisms of separable states},
Year = {2009},
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@article{Rudolph:2009tg,
Abstract = {A simple construction is presented which allows computing the transition amplitude of a quantum circuit to be encoded as computing the permanent of a matrix which is of size proportional to the number of quantum gates in the circuit. This opens up some interesting classical monte-carlo algorithms for approximating quantum circuits.},
Author = {Rudolph, Terry},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.3005},
Keywords = {quantum computing; complexity},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Rudolph/A simple encoding of a quantum circuit amplitude.pdf},
Title = {A simple encoding of a quantum circuit amplitude as a matrix permanent},
Year = {2009},
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@article{Borisov:2009ai,
Abstract = {The theory of operads, defined through categories of labeled graphs, is generalized to suit definitions of higher categories with arbitrary basic shapes. Constructions of cubical, globular and opetopic weak higher categories are obtained as examples.},
Author = {Borisov, Dennis},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.2534},
Keywords = {category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Borisov/Comparing definitions of weak higher categories,.pdf},
Title = {Comparing definitions of weak higher categories, I},
Year = {2009},
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@article{Durham:2009kl,
Abstract = {Birkhoff's Theorem states that doubly stochastic matrices are convex combinations of permutation matrices. Quantum mechanically these matrices are doubly stochastic channels, i.e. they are completely positive maps preserving both the trace and the identity. We expect these channels to be convex combinations of unitary channels and yet it is known that some channels cannot be written that way. Recent work has focused on asymptotic approximations with two specific cases having been proven, but a general theory as yet exists. In this paper we make further progress toward this goal by employing a mix of group and category theory to show that $n(n+1)/2$ copies of an invertible unital quantum channel are isomorphic to $n$ copies of the SU(1) group. In category theory SU(1) has properties similar to those possessed by Hermitian operators in operator theory, thus unital quantum channels behave something like Hermitian operators. In addition, we prove that, in the limit of classical information, these quantum channels behave classically, as expected.},
Author = {Durham, Ian T.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0905.4760},
Keywords = {category theory; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Durham/A category theoretic approach to asymptotic quantum.pdf},
Title = {A category theoretic approach to asymptotic quantum channel approximation and Birkhoff's Theorem},
Year = {2009},
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@incollection{Brukner:2010qe,
Abstract = {Efforts to construct deeper, realistic, level of physical description, in which individual systems have, like in classical physics, preexisting properties revealed by measurements are known as hidden-variable programs. Demonstrations that a hidden-variable program necessarily requires outcomes of certain experiments to disagree with the predictions of quantum theory are called "no-go theorems". The Bell theorem excludes local hidden variable theories. The Kochen-Specker theorem excludes noncontextual hidden variable theories. In local hidden-variable theories faster-that-light-influences are forbidden, thus the results for a given measurement (actual, or just potentially possible) are independent of the settings of other measurement devices which are at space-like separation. In noncontextual hidden-variable theories the predetermined results of a (degenerate) observable are independent of any other observables that are measured jointly with it. It is a fundamental doctrine of quantum information science that quantum communication and quantum computation outperforms their classical counterparts. If this is to be true, some fundamental quantum characteristics must be behind better-than-classical performance of information processing tasks. This chapter aims at establishing connections between certain quantum information protocols and foundational issues in quantum theory. After a brief discusion of the most common misinterpretations of Bell's theorem and a discussion of what its real meaning is, it will be demonstrated how quantum contextuality and violations of local realism can be used as useful resources in quantum information applications.},
Author = {Brukner, Caslav and Zukowski, Marek},
Booktitle = {Handbook of Natural Computing},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Rozenberg, G. and Baeck, T.H.W. and Kok, J.N.},
Eprint = {arXiv:0909.2611},
Keywords = {quantum theory; entanglement; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Brukner/Bell's Inequalities: Foundations and Quantum Communication.pdf},
Publisher = {Springer},
Title = {Bell's Inequalities: Foundations and Quantum Communication},
Year = {2010},
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@article{Kieling:2009oq,
Abstract = {As primitives for entanglement generation, controlled phase gates take a central role in quantum computing. Especially in ideas realizing instances of quantum computation in linear optical gate arrays a closer look can be rewarding. In such architectures, all effective non-linearities are induced by measurements: Hence the probability of success is a crucial parameter of such quantum gates. In this note, we discuss this question for controlled phase gates that implement an arbitrary phase with one and two control qubits. Within the class of post-selected gates in dual-rail encoding with vacuum ancillas we identify the optimal success probabilities. We construct networks that allow for an implementation by means of todays experimental capabilities in detail. The methods employed here appear specifically useful with the advent of integrated linear optical circuits, providing stable interferometers on monolithic structures.},
Author = {Kieling, K. and Eisert, J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.2057},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Kieling/On photonic controlled phase gates.pdf},
Title = {On photonic controlled phase gates},
Year = {2009},
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@article{Dosen:2009eu,
Abstract = {This paper provides geometrical descriptions of the Frobenius monad freely generated by a single object. These descriptions are related to results connecting Frobenius algebras and topological quantum field theories. In these descriptions, which are based on coherence results for self-adjunctions (adjunctions where an endofunctor is adjoint to itself), ordinals in epsilon zero play a prominent role. The paper ends by considering how the notion of Frobenius algebra induces the collapse of the hierarchy of ordinals in epsilon zero, and by raising the question of the exact categorial abstraction of the notion of Frobenius algebra.},
Author = {Dosen, K. and Petric, Z.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0809.2495},
Keywords = {category theory, topology},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Dosen/Ordinals in Frobenius Monads.pdf},
Title = {Ordinals in Frobenius Monads},
Year = {2009},
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@article{Short:2009nx,
Abstract = {Measurements on entangled quantum states can produce outcomes that are nonlocally correlated. But according to Tsirelson's theorem, there is a quantitative limit on quantum nonlocality. It is interesting to explore what would happen if Tsirelson's bound were violated. To this end, we consider a model that allows arbitrary nonlocal correlations, colloquially referred to as "box world". We show that while box world allows more highly entangled states than quantum theory, measurements in box world are rather limited. As a consequence there is no entanglement swapping, teleportation or dense coding.},
Author = {Short, Anthony J. and Barrett, Jonathan},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.2601},
Keywords = {quantum theory, alternative physical models},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Short/Strong nonlocality: A trade-off between states.pdf},
Title = {Strong nonlocality: A trade-off between states and measurements},
Year = {2009},
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@article{Higgins:2009eu,
Abstract = {We present theory and experiment for the task of discriminating two nonorthogonal states, given multiple copies. We implement several local measurement schemes, on both pure states and states mixed by depolarizing noise. We find that schemes which, without noise, are optimal (or have optimal scaling), perform worse with noise than simply repeating the optimal single-copy measurement. Applying optimal control theory, we derive the globally optimal local measurement strategy, which outperforms all other local schemes, and experimentally implement it for various levels of noise.},
Author = {Higgins, B. L. and Booth, B. M. and Doherty, A. C. and Bartlett, S. D. and Wiseman, H. M. and Pryde, G. J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.1572},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Higgins/Mixed state discrimination using optimal.pdf},
Title = {Mixed state discrimination using optimal control},
Year = {2009},
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@article{Jennings:2009nx,
Abstract = {Recently, a substantial amount of debate has grown up around a proposed quantum resolution to the `arrow of time dilemma' that is based on the role of classical memory records of entropy-decreasing events. In this note we show that the argument is incomplete and furthermore, by providing a counter-example, argue that it is incorrect. Instead of quantum mechanics providing a resolution in the manner suggested, it allows enhanced classical memory records of entropy-decreasing events.},
Author = {Jennings, David and Rudolph, Terry},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.1726},
Keywords = {quantum theory; physics},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Jennings/Comment on `Quantum resolution to the arrow of time.pdf},
Title = {Comment on `Quantum resolution to the arrow of time dilemma'},
Year = {2009},
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@article{Werner:2000rt,
Abstract = {We establish a one-to-one correspondence between (1) quantum teleportation schemes, (2) dense coding schemes, (3) orthonormal bases of maximally entangled vectors, (4) orthonormal bases of unitary operators with respect to the Hilbert-Schmidt scalar product, and (5) depolarizing operations, whose Kraus operators can be chosen to be unitary. The teleportation and dense coding schemes are assumed to be ``tight'' in the sense that all Hilbert spaces involved have the same finite dimension d, and the classical channel involved distinguishes d^2 signals. A general construction procedure for orthonormal bases of unitaries, involving Latin Squares and complex Hadamard Matrices is also presented.},
Author = {Werner, R. F.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1088/0305-4470/34/35/332},
Eprint = {arXiv:quant-ph/0003070},
Journal = {Journal of Physics A : mathematical and general},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Werner/All Teleportation and Dense Coding Schemes.pdf},
Pages = {7081-7094},
Title = {All Teleportation and Dense Coding Schemes},
Volume = {34},
Year = {2001},
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Bdsk-Url-1 = {http://dx.doi.org/10.1088/0305-4470/34/35/332}}
@article{Liang:2009vn,
Abstract = {We show that spatially separated parties who perform local measurements on a maximally-entangled state using randomly chosen measurement bases can, with significant probability, generate nonclassical correlations that violate a Bell inequality. For n parties using a Greenberger-Horne-Zeilinger state, this probability of violating a Bell inequality asymptotically tends to unity as the number of parties increases. We also show that, even with both a randomly chosen two-qubit pure state and randomly chosen measurement bases, a violation can be found about 10% of the time.},
Author = {Liang, Yeong-Cherng and Harrigan, Nicholas and Bartlett, Stephen D. and Rudolph, Terry},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Liang/Nonclassical correlations from randomly chosen.pdf},
Title = {Nonclassical correlations from randomly chosen local measurements},
Year = {2009},
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@article{Rau:2009yq,
Abstract = {I show that quantum theory is the only probabilistic framework that permits arbitrary processes to be emulated by sequences of local measurements. This supports the view that, contrary to conventional wisdom, measurement should not be regarded as a complex phenomenon in need of a dynamical explanation but rather as a primitive -- and perhaps the only primitive -- operation of the theory.},
Author = {Rau, Jochen},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.1036},
Keywords = {quantum computing; quantum theory; entanglement; alternative physical models},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Rau/Measurement-based quantum foundations.pdf},
Title = {Measurement-based quantum foundations},
Year = {2009},
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@article{Stirling:2009kx,
Abstract = {This is the first paper in a series where we generalize the Categorical Quantum Mechanics program (due to Abramsky, Coecke, et al) to braided systems. In our view a uniform description of quantum information for braided systems has not yet emerged. The picture is complicated by a diversity of examples that lacks a unifying framework for proving theorems and discovering new protocols. We use category theory to construct a high-level language that abstracts the quantum mechanical properties of braided systems. We exploit this framework to propose an axiomatic description of braided quantum information intended for topological quantum computation. In this installment we first generalize the primordial Abramsky-Coecke "quantum information flow" paradigm from compact closed categories to right-rigid strict monoidal categories. We then study dagger structures for rigid and/or braided categories and formulate a graphical dagger calculus. We then propose two generalizations of strongly compact closed categories. Finally we study partial traces in the context of dagger categories.},
Author = {Stirling, Spencer D. and Wu, Yong-Shi},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.0988},
Keywords = {categorical quantum mechanics; quantum theory; category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Stirling/Braided Categorical Quantum Mechanics I.pdf},
Title = {Braided Categorical Quantum Mechanics I},
Year = {2009},
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@article{Loukopoulos:2009kx,
Abstract = {We introduce a scheme for secure multi-party computation utilising the quantum correlations of entangled states. First we present a scheme for two-party computation, exploiting the correlations of a Greenberger-Horne-Zeilinger state to provide, with the help of a third party, a near-private computation scheme. We then present a variation of this scheme which is passively secure with threshold t=2, in other words, remaining secure when pairs of players conspire together provided they faithfully follow the protocol. We show that this can be generalised to computations of n-party polynomials of degree 2 with a threshold of n-1. The threshold achieved is significantly higher than the best known classical threshold, which satisfies the bound t<n/2.},
Author = {Loukopoulos, Klearchos and Browne, Daniel E.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0906.2297},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Loukopoulos/Secure Multi-Party Computation with a Dishonest.pdf},
Title = {Secure Multi-Party Computation with a Dishonest Majority via Quantum Means},
Year = {2009},
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@article{Sarvepalli:2009jt,
Abstract = {A secret sharing scheme is a cryptographic protocol to distribute a secret state in an encoded form among a group of players such that only authorized subsets of the players can reconstruct the secret. Classically, efficient secret sharing schemes have been shown to be induced by matroids. Furthermore, such matroids can be characterized by an excluded minor relation. No such relations are known for quantum secret sharing schemes. In this paper we take the first steps toward a matroidal characterization of quantum secret sharing schemes. In addition to providing a new perspective on quantum secret sharing schemes, this characterization has important benefits. While previous work has shown how to construct quantum secret sharing schemes for general access structures, these schemes are not claimed to be efficient. In this context the present results prove to be useful; they enable us to construct efficient quantum secret sharing schemes for many general access structures. More precisely, we show that an identically self-dual matroid that is representable over a finite field induces a pure state quantum secret sharing scheme with information rate one.},
Author = {Sarvepalli, Pradeep and Raussendorf, Robert},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0909.0549},
Keywords = {quantum computing;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Sarvepalli/Matroids and Quantum Secret Sharing Schemes.pdf},
Title = {Matroids and Quantum Secret Sharing Schemes},
Year = {2009},
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@article{Planat:2009pi,
Abstract = {In quantum information context, the groups generated by Pauli spin matrices, and Dirac gamma matrices, are known as the single qubit Pauli group P, and two-qubit Pauli group P2, respectively. It has been found [M. Socolovsky, Int. J. Theor. Phys. 43, 1941 (2004)] that the CPT group of the Dirac equation is isomorphic to P. One introduces a two-qubit entangling orthogonal matrix S basically related to the CPT symmetry. With the aid of the two-qubit swap gate, the S matrix allows the generation of the three-qubit real Clifford group and, with the aid of the Toffoli gate, the Weyl group W(E8) is generated (M. Planat, Preprint 0904.3691). In this paper, one derives three-qubit entangling groups ? P and ? P2, isomorphic to the CPT group P and to the Dirac group P2, that are embedded into W(E8). One discovers a new class of pure theequbit quantum states with no-vanishing concurrence and three-tangle that we name CPT states. States of the GHZ and CPT families, and also chain-type states, encode the new representation of the Dirac group and its CPT subgroup},
Author = {Planat, Michel},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0906.1063},
Keywords = {quantum theory; entanglement; algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Planat/Three-qubit entangled embeddings of CPT and Dirac groups.pdf},
Title = {Three-qubit entangled embeddings of CPT and Dirac groups within E8 Weyl group},
Year = {2009},
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@article{Stuckey:2009yq,
Abstract = {We propose a new interpretation of quantum field theory (QFT) based on our interpretation of non-relativistic quantum mechanics called Relational Blockworld. In our interpretation, QFT is the continuous approximation of a more fundamental, discrete theory whereby the transition amplitude Z is not viewed as a sum over all paths in configuration space, but is a mathematical machine for measuring the symmetry of the differential operator and source vector of the discrete action in determining the relative locations of individual detector clicks. We propose that the differential operator and source vector of the underlying discrete theory are related via a self-consistency criterion (SCC) based on a discrete counterpart to the identity that underwrites divergence-free sources in classical field theory, i.e., the boundary of a boundary is zero. Thereby Z is constructed from the SCC, rather than classical field theory, and QFT is the continuous approximation using trajectories, rather than individual detector clicks, as the fundamental entities. In order to illustrate this interpretation, we construct a candidate for the SCC using a discrete path integral formalism over graphs. In this specific approach, the SCC is a tautology, based on the boundary of a boundary is zero, that ensures the source vector is divergence-free and resides in the row space of the differential operator. Accordingly, the differential operator will necessarily have an eigenvector with eigenvalue zero, so the SCC is the origin of gauge invariance. Using this formalism, we obtain the two-source transition amplitude over a (1+1)-dimensional graph with N vertices fundamental to the scalar Gaussian theory.},
Author = {Stuckey, W.M. and McDevitt, Timothy and Silberstein, Michael},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0908.4348},
Keywords = {quantum theory; alternative physical models},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Stuckey/Relational Blockworld Interpretation of Quantum Field.pdf},
Title = {Relational Blockworld Interpretation of Quantum Field Theory},
Year = {2009},
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@article{Baez:2009kx,
Abstract = {Groupoidification is a form of categorification in which vector spaces are replaced by groupoids, and linear operators are replaced by spans of groupoids. We introduce this idea with a detailed exposition of "degroupoidification": a systematic process that turns groupoids and spans into vector spaces and linear operators. Then we present three applications of groupoidification. The first is to Feynman diagrams. The Hilbert space for the quantum harmonic oscillator arises naturally from degroupoidifying the groupoid of finite sets and bijections. This allows for a purely combinatorial interpretation of creation and annihilation operators, their commutation relations, field operators, their normal-ordered powers, and finally Feynman diagrams. The second application is to Hecke algebras. We explain how to groupoidify the Hecke algebra associated to a Dynkin diagram whenever the deformation parameter q is a prime power. We illustrate this with the simplest nontrivial example, coming from the A2 Dynkin diagram. In this example we show that the solution of the Yang-Baxter equation built into the A2 Hecke algebra arises naturally from the axioms of projective geometry applied to the projective plane over the finite field with q elements. The third application is to Hall algebras. We explain how the standard construction of the Hall algebra from the category of representations of a simply-laced quiver can be seen as an example of degroupoidification. This in turn provides a new way to categorify - or more precisely, groupoidify - the positive part of the quantum group associated to the quiver.},
Author = {Baez, John C. and Hoffnung, Alexander E. and Walker, Christopher D.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0908.4305},
Keywords = {category theory; groupoids;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Baez/Higher-Dimensional Algebra VII: Groupoidification.pdf},
Title = {Higher-Dimensional Algebra VII: Groupoidification},
Year = {2009},
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@incollection{Abramsky:2008kx,
Abstract = {This invited chapter in the Handbook of Quantum Logic and Quantum Structures consists of two parts: 1. A substantially updated version of quant-ph/0402130 by the same authors, which initiated the area of categorical quantum mechanics, but had not yet been published in full length; 2. An overview of the progress which has been made since then in this area.},
Author = {Abramsky, Samson and Coecke, Bob},
Booktitle = {Handbook of Quantum Logic and Quantum Structures},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0808.1023},
Keywords = {categorical quantum mechanics; category theory; quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Abramsky/Categorical quantum mechanics.pdf},
Publisher = {Elsevier},
Title = {Categorical quantum mechanics},
Volume = {II},
Year = {2008},
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@article{Hubener:2009ai,
Abstract = {We present general mappings between classical spin systems and quantum physics. More precisely, we show how to express partition functions and correlation functions of arbitrary classical spin models as inner products between quantum stabilizer states and product states, thereby generalizing mappings for some specific models established in [Phys. Rev. Lett. 98, 117207 (2007)]. For Ising- and Potts-type models with and without external magnetic field, we show how the entanglement features of the corresponding stabilizer states are related to the interaction pattern of the classical model, while the choice of product states encodes the details of interaction. These mappings establish a link between the fields of classical statistical mechanics and quantum information theory, which we utilize to transfer techniques and methods developed in one field to gain insight into the other. For example, we use quantum information techniques to recover well known duality relations and local symmetries of classical models in a simple way, and provide new classical simulation methods to simulate certain types of classical spin models. We show that in this way all inhomogeneous models of q-dimensional spins with pairwise interaction pattern specified by a graph of bounded tree-width can be simulated efficiently. Finally, we show relations between classical spin models and measurement-based quantum computation.},
Author = {H{\"u}bener, R. and den Nest, M. Van and D{\"u}r, W. and Briegel, H. J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0812.2127},
Journal = {J. Math. Phys},
Keywords = {quantum computing; quantum many-body; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Hübener/Classical spin systems and the quantum stabilizer.pdf},
Number = {083303},
Title = {Classical spin systems and the quantum stabilizer formalism: general mappings and applications},
Volume = {50},
Year = {2009},
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@article{D.-Hanneke:2009kl,
Abstract = {The universal quantum computer is a device capable of simulating any physical system and represents a major goal for the field of quantum information science. Algorithms performed on such a device are predicted to offer significant gains for some important computational tasks. In the context of quantum information, "universal" refers to the ability to perform arbitrary unitary transformations in the system's computational space. The combination of arbitrary single-quantum-bit (qubit) gates with an entangling two-qubit gate is a gate set capable of achieving universal control of any number of qubits, provided that these gates can be performed repeatedly and between arbitrary pairs of qubits. Although gate sets have been demonstrated in several technologies, they have as yet been tailored toward specific tasks, forming a small subset of all unitary operators. Here we demonstrate a programmable quantum processor that realises arbitrary unitary transformations on two qubits, which are stored in trapped atomic ions. Using quantum state and process tomography, we characterise the fidelity of our implementation for 160 randomly chosen operations. This universal control is equivalent to simulating any pairwise interaction between spin-1/2 systems. A programmable multi-qubit register could form a core component of a large-scale quantum processor, and the methods used here are suitable for such a device.},
Author = {Hanneke, D. and Home, J. P. and Jost, J. D. and Amini, J. M. and Leibfried, D. and Wineland, D. J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0908.3031},
Keywords = {quantum computing;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/D. Hanneke/Realisation of a programmable two-qubit quantum processor.pdf},
Title = {Realisation of a programmable two-qubit quantum processor},
Year = {2009},
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@article{Cesar-Dominguez:2009qe,
Abstract = {This paper provides an abstract definition of some kinds of logics, called diagrammatic logics, together with a definition of morphisms and of 2-morphisms between diagrammatic logics. The definition of the 2-category of diagrammatic logics rely on category theory, mainly on adjunction, categories of fractions and limit sketches. This framework is applied to the formalization of a parameterization process. This process, which consists in adding a formal parameter to some operations in a given specification, is presented as a morphism of logics. Then the parameter passing process, for recovering a model of the given specification from a model of the parameterized specification and an actual parameter, is seen as a 2-morphism of logics.},
Author = {Dominguez, Cesar and Duval, Dominique},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0908.3737},
Keywords = {categorical logic; graphical calculi},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Cesar Dominguez/Diagrammatic logic applied to a parameterization process.pdf},
Title = {Diagrammatic logic applied to a parameterization process},
Year = {2009},
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@techreport{Hooft:2009oq,
Abstract = {Investigating a class of models that is familiar in studies of cellular automata, we find that quantum operators can be employed to describe their long distance behavior. These operators span a Hilbert space that appears to turn such a model into a genuine quantum field theory, obeying the usual conditions of locality in terms of its quantum commutators. Entangled states can be constructed exactly as in quantum theories. This raises the question whether such models allow Bell's inequalities to be violated. Being a local, deterministic theory, one would argue that this is impossible, but since at large distance scales the model does not seem to differ from real quantum field theories, there is reason to wonder why it should not allow entangled states. The standard arguments concerning Bell's inequalities are re-examined in this light.},
Author = {{'t Hooft}, Gerard},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0908.3408},
Institution = {Institute for Theoretical Physics, Utrecht University},
Keywords = {quantum theory; alternative physical models; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Hooft/Entangled quantum states in a local deterministic.pdf},
Number = {ITP-UU-09/77, SPIN-09/30},
Title = {Entangled quantum states in a local deterministic theory},
Year = {2009},
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@article{Schulz:2009eu,
Abstract = {In 1985, Edward Nelson, who formulated the theory of stochastic mechanics, made an interesting remark on Bell's theorem. Nelson analysed the latter in the light of classical fields that behave randomly. He found that if a stochastic hidden variable theory fulfils certain conditions, the inequality of Bell can be violated. Moreover, Nelson was able to prove that this may happen without any instantaneous communication between the two spatially separated measurement stations. Since Nelson's article got almost overlooked by physicists, we try to review his comments on Bell's theorem. We argue that a modification of stochastic mechanics published recently by Fritsche and Haugk can be extended to a theory which fulfils the requirements of Nelson's analysis. The article proceeds to derive the quantum mechanical formalism of spinning particles and the Pauli equation from this version of stochastic mechanics. Then, we investigate Bohm's version of the EPR experiment. Additionally, other setups, like entanglement swapping or time and position correlations, are shortly explained from the viewpoint of our local hidden-variable model. Finally, we mention that this theory could perhaps be relativistically extended.},
Author = {Schulz, Benjamin},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1002/andp.200810345},
Eprint = {arXiv:0807.3369},
Journal = {Annalen der Physik},
Keywords = {quantum theory; alternative physical models; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Schulz/A new look at Bell's inequalities and Nelson's theorem.pdf},
Number = {4},
Title = {A new look at Bell's inequalities and Nelson's theorem},
Volume = {18},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1002/andp.200810345}}
@article{Maccone:2009nx,
Abstract = {The arrow of time dilemma: the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e. entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace},
Author = {Maccone, Lorenzo},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1103/PhysRevLett.103.080401},
Eprint = {arXiv:0802.0438},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum theory; physics},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Maccone/A quantum solution to the arrow-of-time dilemma.pdf},
Number = {080401},
Title = {A quantum solution to the arrow-of-time dilemma},
Volume = {103},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.103.080401}}
@article{Nitu-Kitchloo:2010kb,
Abstract = {The Madsen-Tillmann spectra defined by categories of three- and four-dimensional Spin manifolds have a very rich algebraic structure, whose surface is scratched here.},
Author = {Kitchloo, Nitu and Morava, Jack},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0908.3114},
Journal = {Pure and Applied Mathematics Quarterly},
Keywords = {category theory; quantum gravity; algebra; topology},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Kitchloo/Spin cobordism categories in low dimensions.pdf},
Number = {2},
Pages = {1-13},
Title = {Spin cobordism categories in low dimensions},
Volume = {6},
Year = {2010},
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@article{Joyal:2009la,
Abstract = {We describe a category of Feynman graphs and show how it relates to compact symmetric multicategories (coloured modular operads) just as linear orders relate to categories and rooted trees relate to multicategories. More specifically we obtain the following nerve theorem: compact symmetric multicategories can be characterised as presheaves on the category of Feynman graphs subject to a Segal condition. This text is a write-up of the second-named author's QPL6 talk; a more detailed account of this material will appear elsewhere.},
Author = {Joyal, Andr{\'e} and Kock, Joachim},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0908.2675},
Keywords = {category theory; polycategories; compact closed categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Joyal/Feynman graphs, and nerve theorem for compact.pdf},
Title = {Feynman graphs, and nerve theorem for compact symmetric multicategories},
Year = {2009},
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@article{Jean-Daniel-Bancal:2009fy,
Abstract = {Reproducing with elementary resources the correlations that arise when a quantum system is measured (quantum state simulation), allows one to get insight on the operational and computational power of quantum correlations. We propose a family of models that can simulate von Neumann measurements in the x-y plane of the Bloch sphere on n-partite GHZ states.},
Author = {Bancal, Jean-Daniel and Branciard, Cyril and Gisin, Nicolas},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0908.2640},
Keywords = {quantum computing; entanglement},
Title = {Simulation of equatorial von Neumann measurements on GHZ states using nonlocal resources},
Year = {2009}}
@article{Campbell:2009bs,
Abstract = {Magic state distillation is an important primitive in fault-tolerant quantum computation. The magic states are pure non-stabilizer states which can be distilled from certain mixed non-stabilizer states via Clifford group operations alone. Due to the Gottesman-Knill theorem, convex mixtures of Pauli eigenstates are not expected to be magic state distillable, but it has been an open question whether all mixed states outside this octahedral set may be distilled. In this Letter we show that, when resources are finitely limited, non-distillable states exist outside the stabilizer octahedron. In analogy with the bound entangled states, which arise in entanglement theory, we call such states bound states for magic state distillation.},
Author = {Campbell, Earl T. and Browne, Dan E.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0908.0836},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Campbell/Bound States for Magic State Distillation.pdf},
Title = {Bound States for Magic State Distillation},
Year = {2009},
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@inproceedings{Campbell:2009it,
Abstract = {We present a theorem that shows that all useful protocols for magic state distillation output states with a fidelity that is upper-bounded by those generated by a much smaller class of protocols. This reduced class consists of the protocols where multiple copies of a state are projected onto a stabilizer codespace and the logical qubit is then decoded.},
Author = {Campbell, Earl T. and Browne, Dan E.},
Booktitle = {Proceedings of TQC 2009},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0908.0838v2},
Keywords = {quantum computing;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Campbell/On the Structure of Protocols for Magic State Distillation.pdf},
Publisher = {Springer},
Series = {LNCS},
Title = {On the Structure of Protocols for Magic State Distillation},
Year = {2009},
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@incollection{Coecke:2009db,
Abstract = {In recent work, symmetric dagger-monoidal (SDM) categories have emerged as a convenient categorical formalization of quantum mechanics. The objects represent physical systems, the morphisms physical operations, whereas the tensors describe composite systems. Classical data turn out to correspond to Frobenius algebras with some additional properties. They express the distinguishing capabilities of classical data: in contrast with quantum data, classical data can be copied and deleted. The algebraic approach thus shifts the paradigm of "quantization" of a classical theory to "classicization" of a quantum theory. Remarkably, the simple SDM framework suffices not only for this conceptual shift, but even allows us to distinguish the deterministic classical operations (i.e. functions) from the nondeterministic classical operations (i.e. relations), and the probabilistic classical operations (stochastic maps). Moreover, a combination of some basic categorical constructions (due to Kleisli, resp. Grothendieck) with the categorical presentations of quantum states, provides a resource sensitive account of various quantum-classical interactions: of classical control of quantum data, of classical data arising from quantum measurements, as well as of the classical data processing in-between controls and measurements. A salient feature here is the graphical calculus for categorical quantum mechanics, which allows a purely diagrammatic representation of classical-quantum interaction.},
Author = {Coecke, Bob and Paquette, Eric Oliver and Pavlovic, Dusko},
Booktitle = {Semantic Techniques in Quantum Computation},
Chapter = {2},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Gay, S. and Mackie, I.},
Eprint = {arXiv:0904.1997},
Keywords = {categorical quantum mechanics; monoidal categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Coecke/Classical and quantum structuralism.pdf},
Pages = {29--69},
Publisher = {Cambridge University Press},
Title = {Classical and quantum structuralism},
Year = {2010},
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@inproceedings{Pavlovic:2008rt,
Abstract = {In categorical quantum mechanics, classical structures characterize the classical interfaces of quantum resources on one hand, while on the other hand giving rise to some quantum phenomena. In the standard Hilbert space model of quantum theories, classical structures over a space correspond to its orthonormal bases. In the present paper, we show that classical structures in the category of relations correspond to biproducts of abelian groups. Although relations are, of course, not an interesting model of quantum computation, this result has some interesting computational interpretations. If relations are viewed as denotations of nondeterministic programs, it uncovers a wide variety of non-standard quantum structures in this familiar area of classical computation. Ironically, it also opens up a version of what in philosophy of quantum mechanics would be called an ontic-epistemic gap, as it provides no direct interface to these nonstandard quantum structures.},
Author = {Pavlovic, Dusko},
Booktitle = {3rd International Symposium on Quantum Interaction - QI 2009},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1007/978-3-642-00834-4_13},
Eprint = {arXiv:0812.2266},
Keywords = {categorical quantum mechanics; algebra; mutually unbiased bases},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Pavlovic/Quantum and classical structures in nondeterminstic computation.pdf},
Pages = {143-157},
Series = {Lecture Notes in Computer Science},
Title = {Quantum and classical structures in nondeterminstic computation},
Volume = {5494},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-00834-4_13}}
@article{Gisin:ly,
Abstract = {The claim that the observation of a violation of a Bell inequality leads to an alleged alternative between nonlocality and non-realism is annoying because of the vagueness of the second term.},
Author = {Gisin, Nicolas},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0901.4255},
Keywords = {quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Gisin/Non-realism : deep thought or a soft option.pdf},
Title = {Non-realism : deep thought or a soft option ?},
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@article{Bogusaw-Broda:2009zr,
Abstract = {It has been shown that there is a small possibility to experimentally violate the CHSH Bell inequality in a 'classical' context. The probability of such a violation has been estimated in the framework of a classical probabilistic model in the language of a random-walk representation.},
Author = {Broda, Bogus{\l}aw and Szanecki, Micha{\l}},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0905.0398},
Keywords = {quantum theory; alternative physical models;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Broda/On possible violation of the CHSH Bell inequality.pdf},
Title = {On possible violation of the CHSH Bell inequality in a classical context},
Year = {2009},
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@article{Duchamp:2009fr,
Abstract = {Starting with the Heisenberg-Weyl algebra, fundamental to quantum physics, we first show how the ordering of the non-commuting operators intrinsic to that algebra gives rise to generalizations of the classical Stirling Numbers of Combinatorics. These may be expressed in terms of infinite, but {\em row-finite}, matrices, which may also be considered as endomorphisms of $\C[[x]]$. This leads us to consider endomorphisms in more general spaces, and these in turn may be expressed in terms of generalizations of the ladder-operators familiar in physics.},
Author = {Duchamp, G{\'e}rard Henry Edmond and Poinsot, Laurent and Solomon, Allan I. and Penson, Karol A. and Blasiak, Pawel and Horzela, Andrzej},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0908.2332},
Keywords = {algebra; quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Duchamp/Ladder Operators and Endomorphisms in Combinatorial Physics.pdf},
Title = {Ladder Operators and Endomorphisms in Combinatorial Physics},
Year = {2009},
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@article{Karlsson:2009ys,
Abstract = {A new, two-parameter, nonaffine family of complex Hadamard matrices of order 6 is reported. It interpolates between the two Fourier families, and contains as one-parameter subfamilies the Dita family, a symmetric family and an almost (up to equivalence) self-adjoint family.},
Author = {Karlsson, Bengt R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0908.2555},
Keywords = {mutually unbiased bases; algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Karlsson/Two-parameter complex Hadamard matrices for N=6.pdf},
Title = {Two-parameter complex Hadamard matrices for N=6},
Year = {2009},
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@article{Havlicek:2009rt,
Abstract = {Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce gradually necessary and sufficient conditions to be met in order to carry out the following programme: Given a group $\vG$, we first construct vector spaces over $\GF(p)$, $p$ a prime, by factorising $\vG$ over appropriate normal subgroups. Then, by expressing $\GF(p)$ in terms of the commutator subgroup of $\vG$, we construct alternating bilinear forms, which reflect whether or not two elements of $\vG$ commute. Restricting to $p=2$, we search for ``refinements'' in terms of quadratic forms, which capture the fact whether or not the order of an element of $\vG$ is $\leq 2$. Such factor-group-generated vector spaces admit a natural reinterpretation in the language of symplectic and orthogonal polar spaces, where each point becomes a ``condensation'' of several distinct elements of $\vG$. Finally, several well-known physical examples (single- and two-qubit Pauli groups, both the real and complex case) are worked out in detail to illustrate the fine traits of the formalism.},
Author = {Havlicek, Hans and Odehnal, Boris and Saniga, Metod},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0903.5418},
Keywords = {quantum theory; mutually unbiased bases; algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Havlicek/Factor-Group-Generated Polar Spaces and (Multi-)Qudits.pdf},
Title = {Factor-Group-Generated Polar Spaces and (Multi-)Qudits},
Year = {2009},
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@article{Korepin:2009vn,
Abstract = {This article reviews the quantum entanglement in Valence-Bond-Solid (VBS) states defined on a lattice or a graph. The subject is presented in a self-contained and pedagogical way. The VBS state was first introduced in the celebrated paper by I. Affleck, T. Kennedy, E. H. Lieb and H. Tasaki (abbreviation AKLT is widely used). It became essential in condensed matter physics and quantum information (measurement-based quantum computation). Many publications have been devoted to the subject. Recently entanglement was studied in the VBS state. In this review we start with the definition of a general AKLT spin chain and the construction of VBS ground state. In order to study entanglement, a block subsystem is introduced and described by the density matrix. Density matrices of 1-dimensional models are diagonalized and the entanglement entropies (the von Neumann entropy and Renyi entropy) are calculated. In the large block limit, the entropies also approach finite limits. Study of the spectrum of the density matrix led to the discovery that the density matrix is proportional to a projector.},
Author = {Korepin, Vladimir E. and Xu, Ying},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0908.2345},
Keywords = {quantum many-body; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Korepin/Entanglement in Valence-Bond-Solid States.pdf},
Title = {Entanglement in Valence-Bond-Solid States},
Year = {2009},
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@article{Fregier:2009yq,
Abstract = {Our main goal in this paper is to translate the diagram relating groups, Lie algebras and Hopf algebras to the corresponding 2-objects, i.e. to categorify it. This is done interpreting 2-objects as crossed modules and showing the compatibility of the standard functors linking groups, Lie algebras and Hopf algebras with the concept of a crossed module. One outcome is the construction of an enveloping algebra of the string Lie algebra of Baez-Crans, another is the clarification of the passage from crossed modules of Hopf algebras to Hopf 2-algebras.},
Author = {Fregier, Yael and Wagemann, Friedrich},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0908.2353},
Keywords = {algebra; category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Fregier/On Hopf 2-algebras.pdf},
Title = {On Hopf 2-algebras},
Year = {2009},
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@article{Vidal:2008kx,
Abstract = {We introduce the multi-scale entanglement renormalization ansatz (MERA), an efficient representation of certain quantum many-body states on a D-dimensional lattice. Equivalent to a quantum circuit with logarithmic depth and distinctive causal structure, the MERA allows for an exact evaluation of local expectation values. It is also the structure underlying entanglement renormalization, a coarse-graining scheme for quantum systems on a lattice that is focused on preserving entanglement.},
Author = {Vidal, G.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1103/PhysRevLett.101.110501},
Eprint = {arXiv:quant-ph/0610099v1},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum computing, quantum many-body, entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Vidal/A class of quantum many-body states that.pdf},
Number = {110501},
Title = {A class of quantum many-body states that can be efficiently simulated},
Volume = {101},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.101.110501}}
@article{Kibler:2009fp,
Abstract = {The construction of unitary operator bases in a finite-dimensional Hilbert space is reviewed through a nonstandard approach combinining angular momentum theory and representation theory of SU(2). A single formula for the bases is obtained from a polar decomposition of SU(2) and analysed in terms of cyclic groups, quadratic Fourier transforms, Hadamard matrices and generalized Gauss sums. Weyl pairs, generalized Pauli operators and their application to the unitary group and the Pauli group naturally arise in this approach.},
Author = {Kibler, Maurice Robert},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0907.2838v1},
Keywords = {quantum computing; quantum theory;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Kibler/An angular momentum approach to quadratic Fourier.pdf},
Title = {An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, unitary group and Pauli group},
Year = {2009},
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@article{Day:2006lq,
Abstract = {We state a Yoneda-type lemma which leads to various functor categories being compact closed.},
Author = {Day, Brian J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:math/0605463v1},
Keywords = {compact closed categories; category theory; monoidal categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Day/Compact convolution.pdf},
Title = {Compact convolution},
Year = {2006},
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@article{Day:2008eu,
Abstract = {It is well known that strong monoidal functors preserve duals. In this short note we show that a slightly weaker version of functor, which we call "Frobenius monoidal", is sufficient.},
Author = {Day, Brian and Pastro, Craig},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0801.4107v2},
Keywords = {category theory; monoidal categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Day/Note on Frobenius monoidal functors.pdf},
Title = {Note on Frobenius monoidal functors},
Year = {2008},
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@article{Day:2007fv,
Abstract = {We show that the (co)endomorphism algebra of a sufficiently separable "fibre" functor into Vect_k, for k a field of characteristic 0, has the structure of what we call a "unital" von Neumann core in Vect_k. For Vect_k, this particular notion of algebra is weaker than that of a Hopf algebra, although the corresponding concept in Set is again that of a group.},
Author = {Day, Brian and Pastro, Craig},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0712.1864v1},
Keywords = {monoidal categories; category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Day/On endomorphism algebras of separable monoidal functors.pdf},
Title = {On endomorphism algebras of separable monoidal functors},
Year = {2007},
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@techreport{Joyal:1986yg,
Author = {Joyal, A. and Street, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Institution = {Macquarie Mathematics Reports},
Keywords = {monoidal categories; category theory;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Joyal/Braid Monoidal Categories.pdf},
Number = {860081},
Title = {Braided Monoidal Categories},
Year = {1986},
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@article{Day:2003zl,
Author = {Day, Brian and Street, Ross},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:math/0301209v2},
Keywords = {groupoids; category theory; monoidal categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Day/Quantum categories, star autonomy, and quantum.pdf},
Title = {Quantum categories, star autonomy, and quantum groupoids},
Year = {2003},
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@article{Day:2007rm,
Abstract = {Association schemes and rational conformal field theories (RCFT's) can each collectively be regarded as a type of Fourier transformation (pseudofunctor). Mathematically this is a fairly straightforward observation, but may be worth pursuing from a physical viewpoint.},
Author = {Day, Brian J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:math/0702208v2},
Keywords = {category theory; monoidal categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Day/Association schemes and classical RCFT's as "graphic".pdf},
Title = {Association schemes and classical RCFT's as "graphic" Fourier transformations},
Year = {2007},
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@techreport{Day:1981rz,
Abstract = {We give a summary (without proofs) of the main results in the author's thesis entitled ``Construction of biclosed categories'' (University of New South Wales, Australia, 1970). This summary is reprinted directly from Report 81-0030 of the School of Mathematics and Physics, Macquarie University, April 1981. In particular, it gives sufficient conditions for existence of an extension of a (pro)monoidal category structure along a given dense functor to a cocomplete category. The two basic procedures used in the proof turn out to be special cases of the final result, the two respective dense functors then being the Yoneda embedding followed by a localisation. The final result has a standard universal property based on left Kan extension of (pro)monoidal functors along the given dense functor, however this property is not stated explicitly here.},
Author = {Day, Brian J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0705.3485v1},
Institution = {School of Mathematics and Physics, Macquarie University},
Keywords = {category theory;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Day/Biclosed bicategories: localisation of convolution.pdf},
Number = {81-0030},
Title = {Biclosed bicategories: localisation of convolution},
Year = {1981},
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@article{Biamonte:2009sf,
Abstract = {The Lorentzian length of a timelike curve connecting both endpoints of a classical computation is a function of the path taken through Minkowski spacetime. The associated runtime difference is due to time-dilation: the phenomenon whereby an observer finds that another's physically identical ideal clock has ticked at a different rate than their own clock. Using ideas appearing in the framework of computational complexity theory, time-dilation is quantified as an algorithmic resource by relating relativistic energy to an $n$th order polynomial time reduction at the completion of an observer's journey. These results enable a comparison between the optimal quadratic \emph{Grover speedup} from quantum computing and an $n=2$ speedup using classical computers and relativistic effects. The goal is not to propose a practical model of computation, but to probe the ultimate limits physics places on computation.},
Author = {Biamonte, Jacob D.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0907.1579v1},
Keywords = {relativity; complexity},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Biamonte/The Computational Power of Minkowski Spacetime.pdf},
Title = {The Computational Power of Minkowski Spacetime},
Year = {2009},
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@article{Coecke:2009rt,
Abstract = {The quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the arrays of 0s and 1s of the early days of computer programming practice. In this review we present steps towards a diagrammatic `high-level' alternative for the Hilbert space formalism, one which appeals to our intuition. It allows for intuitive reasoning about interacting quantum systems, and trivialises many otherwise involved and tedious computations. It clearly exposes limitations such as the no-cloning theorem, and phenomena such as quantum teleportation. As a logic, it supports `automation'. It allows for a wider variety of underlying theories, and can be easily modified, having the potential to provide the required step-stone towards a deeper conceptual understanding of quantum theory, as well as its unification with other physical theories. Specific applications discussed here are purely diagrammatic proofs of several quantum computational schemes, as well as an analysis of the structural origin of quantum non-locality. The underlying mathematical foundation of this high-level diagrammatic formalism relies on so-called monoidal categories, a product of a fairly recent development in mathematics. These monoidal categories do not only provide a natural foundation for physical theories, but also for proof theory, logic, programming languages, biology, cooking, ... The challenge is to discover the necessary additional pieces of structure that allow us to predict genuine quantum phenomena.},
Author = {Coecke, Bob},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1080/00107510903257624},
Eprint = {arXiv:0908.1787},
Journal = {Contemporary Physics},
Keywords = {categorical quantum mechanics; surveys},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Coecke/Quantum Picturalism.pdf},
Month = {january},
Number = {1},
Pages = {59--83},
Title = {Quantum Picturalism},
Volume = {51},
Year = {2010},
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Bdsk-Url-1 = {http://dx.doi.org/10.1080/00107510903257624}}
@article{Seevinck:2009vn,
Abstract = {A fruitful way of studying physical theories is via the question whether the possible physical states and different kinds of correlations in each theory can be shared to different parties. Over the past few years it has become clear that both quantum entanglement and non-locality (i.e., correlations that violate Bell-type inequalities) have limited shareability properties and can sometimes even be monogamous. We give a self-contained review of these results as well as present new results on the shareability of different kinds of correlations, including local, quantum and no-signalling correlations. This includes an alternative simpler proof of the Toner-Verstraete monogamy inequality for quantum correlations, as well as a strengthening thereof. Further, the relationship between sharing non-local quantum correlations and sharing mixed entangled states is investigated, and already for the simplest case of bi-partite correlations and qubits this is shown to be non-trivial. Also, a recently proposed new interpretation of Bell's theorem by Schumacher in terms of shareability of correlations is critically assessed. Finally, the relevance of monogamy of non-local correlations for secure quantum key distribution is pointed out, although, and importantly, it is stressed that not all non-local correlations are monogamous},
Author = {Seevinck, Michael},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0908.1867v1},
Journal = {Quantum Information Processing},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Seevinck/Monogamy of Correlations vs. Monogamy of Entanglement.pdf},
Title = {Monogamy of Correlations vs. Monogamy of Entanglement},
Year = {2009},
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@article{Kassal:2009yq,
Abstract = {It is known that quantum computers, if available, would allow an exponential decrease in the computational cost of quantum simulations. We extend this result to show that the computation of molecular properties (energy derivatives) could also be sped up using quantum computers. We provide a quantum algorithm for the numerical evaluation of molecular properties, whose time cost is a constant multiple of the time needed to compute the molecular energy, regardless of the size of the system. Molecular properties computed with the proposed approach could also be used for the optimization of molecular geometries or other properties. For that purpose, we discuss the benefits of quantum techniques for Newton's method and Householder methods. Finally, global minima for the proposed optimizations can be found using the quantum basin hopper algorithm, which offers an additional quadratic reduction in cost over classical multi-start techniques.},
Author = {Kassal, Ivan and Aspuru-Guzik, Al{\'a}n},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0908.1921},
Keywords = {quantum computing; algorithms},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Kassal/Quantum Algorithm for Molecular Properties and Geometry.pdf},
Title = {Quantum Algorithm for Molecular Properties and Geometry Optimization},
Year = {2009},
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@article{Skrovseth:2009kx,
Abstract = {We consider a one-dimensional spin chain for which the ground state is the cluster state, capable of functioning as a quantum computational wire when subjected to local adaptive measurements of individual qubits, and investigate the robustness of this property to local and coupled (Ising-type) perturbations. We investigate the ground state both by identifying suitable correlation functions as order parameters, as well as numerically using a variational method based on matrix product states. We find that the model retains an infinite localizable entanglement length for Ising and local fields up to a quantum phase transition, but that the resulting entangled state is not simply characterized by a Pauli correction based on the measurement results},
Author = {Skr{\o}vseth, Stein Olav and Bartlett, Stephen D.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1103/PhysRevA.80.022316},
Eprint = {arXiv:0905.1480},
Journal = {Phys. Rev. A},
Keywords = {entanglement, quantum many-body; quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Skrøvseth/Phase transitions and localizable entanglement in cluster-state.pdf},
Number = {022316},
Title = {Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields},
Volume = {80},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.80.022316}}
@article{Jurg-Frohlicha:2006nx,
Abstract = {Much of algebra and representation theory can be formulated in the general framework of tensor categories. The aim of this paper is to further develop this theory for braided tensor categories. Several results are established that do not have a substantial counterpart for symmetric tensor categories. In particular, we exhibit various equivalences involving categories of modules over algebras in ribbon categories. Finally, we establish a correspondence of ribbon categories that can be applied to, and is in fact motivated by, the coset construction in conformal quantum field theory.},
Author = {Fr{\"o}hlich, J{\"u}rg and Fuchs, J{\"u}rgen and Runkel, Ingo and Schweigert, Christoph},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {doi:10.1016/j.aim.2005.04.007},
Journal = {Advances in Mathematics},
Keywords = {category theory; monoidal categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Fröhlich/Correspondences of ribbon categories.pdf},
Month = {January},
Number = {1},
Pages = {192-329},
Robots = {NOINDEX,NOFOLLOW,NOARCHIVE},
Title = {Correspondences of ribbon categories},
Volume = {199},
Year = {2006},
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Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.aim.2005.04.007}}
@article{Bartlett:2007nx,
Abstract = {Recently, there has been much interest in a new kind of ``unspeakable'' quantum information that stands to regular quantum information in the same way that a direction in space or a moment in time stands to a classical bit string: the former can only be encoded using particular degrees of freedom while the latter are indifferent to the physical nature of the information carriers. The problem of correlating distant reference frames, of which aligning Cartesian axes and synchronizing clocks are important instances, is an example of a task that requires the exchange of unspeakable information and for which it is interesting to determine the fundamental quantum limit of efficiency. There have also been many investigations into the information theory that is appropriate for parties that lack reference frames or that lack correlation between their reference frames, restrictions that result in global and local superselection rules. In the presence of these, quantum unspeakable information becomes a new kind of resource that can be manipulated, depleted, quantified, etc. Methods have also been developed to contend with these restrictions using relational encodings, particularly in the context of computation, cryptography, communication, and the manipulation of entanglement. This paper reviews the role of reference frames and superselection rules in the theory of quantum-information processing.},
Author = {Bartlett, S. D. and Rudolph, T. and Spekkens, R. W.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Description = {Recently, there has been much interest in a new kind of ``unspeakable'' quantum information that stands to regular quantum information in the same way that a direction in space or a moment in time stands to a classical bit string: the former can only be encoded using particular degrees of freedom while the latter are indifferent to the physical nature of the information carriers. The problem of correlating distant reference frames, of which aligning Cartesian axes and synchronizing clocks are important instances, is an example of a task that requires the exchange of unspeakable information and for which it is interesting to determine the fundamental quantum limit of efficiency. There have also been many investigations into the information theory that is appropriate for parties that lack reference frames or that lack correlation between their reference frames, restrictions that result in global and local superselection rules. In the presence of these, quantum unspeakable information becomes a new kind of resource that can be manipulated, depleted, quantified, etc. Methods have also been developed to contend with these restrictions using relational encodings, particularly in the context of computation, cryptography, communication, and the manipulation of entanglement. This paper reviews the role of reference frames and superselection rules in the theory of quantum-information processing.},
Doi = {10.1103/RevModPhys.79.555},
Journal = {Rev. Mod. Phys},
Keywords = {quantum computing; entanglement; surveys;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Bartlett/Reference frames, superselection rules, and quantum.pdf},
Number = {555},
Title = {Reference frames, superselection rules, and quantum information},
Volume = {79},
Year = {2007},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/RevModPhys.79.555}}
@article{Lafont:1997fz,
Abstract = {It is shown that a very simple system ofinteraction combinators, with only three symbols and six rules, is a universal model of distributed computation, in a sense that will be made precise. This paper is the continuation of the author's work oninteraction nets, inspired by Girard's proof nets forlinear logic, but no preliminary knowledge of these topics is required for its reading.},
Author = {Lafont, Yves},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Information and Computation},
Keywords = {proof-nets; graphical calculi; linear logic; combinatory logic; rewriting},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Lafont/Interaction Combinators.pdf},
Number = {1},
Pages = {69-101},
Title = {Interaction Combinators},
Volume = {137},
Year = {1997},
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Bdsk-Url-1 = {http://dx.doi.org/10.1006/inco.1997.2643}}
@article{GrossEisert:2007nr,
Abstract = {We establish a framework which allows one to construct novel schemes for measurement-based quantum computation. The technique further develops tools from many-body physics - based on finitely correlated or projected entangled pair states - to go beyond the cluster-state based one-way computer. We identify resource states that are radically different from the cluster state, in that they exhibit non-vanishing correlation functions, can partly be prepared using gates with non-maximal entangling power, or have very different local entanglement properties. In the computational models, the randomness is compensated in a different manner. It is shown that there exist resource states which are locally arbitrarily close to a pure state. Finally, we comment on the possibility of tailoring computational models to specific physical systems as, e.g. cold atoms in optical lattices.},
Author = {Gross, David and Eisert, Jens},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0609149v3},
Journal = {Phys. Rev. Lett.},
Keywords = {entanglement; measurement-based quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Gross/Novel schemes for measurement-based quantum computation.pdf},
Number = {220503},
Title = {Novel schemes for measurement-based quantum computation},
Volume = {98},
Year = {2007},
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@article{Brierley:2009py,
Abstract = {The density matrix of a qudit may be reconstructed with optimal efficiency if the expectation values of a specific set of observables are known. In dimension six, the required observables only exist if it is possible to identify six mutually unbiased complex (6×6) Hadamard matrices. Prescribing a first Hadamard matrix, we construct all others mutually unbiased to it, using algebraic computations performed by a computer program. We repeat this calculation many times, sampling all known complex Hadamard matrices, and we never find more than two that are mutually unbiased. This result adds considerable support to the conjecture that no seven mutually unbiased bases exist in dimension six.},
Author = {Brierley, Stephen and Weigert, Stefan},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Description = {The density matrix of a qudit may be reconstructed with optimal efficiency if the expectation values of a specific set of observables are known. In dimension six, the required observables only exist if it is possible to identify six mutually unbiased complex (6×6) Hadamard matrices. Prescribing a first Hadamard matrix, we construct all others mutually unbiased to it, using algebraic computations performed by a computer program. We repeat this calculation many times, sampling all known complex Hadamard matrices, and we never find more than two that are mutually unbiased. This result adds considerable support to the conjecture that no seven mutually unbiased bases exist in dimension six.},
Eprint = {arXiv:0901.4051v1},
Journal = {Phys. Rev. A},
Keywords = {Hadamard matrices; quantum computing; quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Brierley/Constructing mutually unbiased bases in dimension.pdf},
Number = {052316},
Title = {Constructing mutually unbiased bases in dimension six},
Volume = {79},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.79.052316}}
@article{Tadej:2006pc,
Abstract = {Complex Hadamard matrices, consisting of unimodular entries with arbitrary phases, play an important role in the theory of quantum information. We review basic properties of complex Hadamard matrices and present a catalogue of inequivalent cases known for the dimensions N = 2,..., 16. In particular, we explicitly write down some families of complex Hadamard matrices for N = 12,14 and 16, which we could not find in the existing literature.},
Author = {Tadej, Wojciech and {\.Z}yczkowski, Karol},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0512154v2},
Journal = {Open Systems & Information Dynamics},
Keywords = {Hadamard matrices; mutually unbiased bases},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Tadej/A Concise Guide to Complex Hadamard Matrices.pdf},
Number = {2},
Pages = {133-177},
Title = {A Concise Guide to Complex Hadamard Matrices},
Volume = {13},
Year = {2006},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s11080-006-8220-2}}
@incollection{Duncan:2009cs,
Abstract = {Just as conventional functional programs may be understood as proofs in an intuitionistic logic, so quantum processes can also be viewed as proofs in a suitable logic. We describe such a logic, the logic of compact closed categories and biproducts, presented both as a sequent calculus and as a system of proof-nets. This logic captures much of the necessary structure needed to represent quantum processes under classical control, while remaining agnostic to the fine details. We demonstrate how to represent quantum processes as proof-nets, and show that the dynamic behaviour of a quantum process is captured by the cut-elimination procedure for the logic. We show that the cut elimination procedure is strongly normalising: that is, that every legal way of simplifying a proof-net leads to the same, unique, normal form. Finally, taking some initial set of operations as non-logical axioms, we show that that the resulting category of proof-nets is a representation of the free compact closed category with biproducts generated by those operations.},
Author = {Duncan, Ross},
Booktitle = {Semantic Techniques in Quantum Computation},
Chapter = {3},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0903.5154v1},
Keywords = {categorical quantum mechanics; compact closed categories; proof-nets; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Duncan/Generalised Proof-Nets for Compact Categories with.pdf},
Pages = {70--134},
Publisher = {Cambridge University Press},
Title = {Generalised Proof-Nets for Compact Categories with Biproducts},
Year = {2010},
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@inproceedings{Duncan:2009ph,
Abstract = {Coecke and Duncan recently introduced a categorical formalisation of the interaction of complementary quantum observables. In this paper we use their diagrammatic language to study graph states, a computationally interesting class of quantum states. We give a graphical proof of the fixpoint property of graph states. We then introduce a new equation, for the Euler decomposition of the Hadamard gate, and demonstrate that Van den Nest's theorem--locally equivalent graphs represent the same entanglement--is equivalent to this new axiom. Finally we prove that the Euler decomposition equation is not derivable from the existing axioms.},
Author = {Duncan, Ross and Perdrix, Simon},
Booktitle = {Computability in Europe: Mathematical Theory and Computational Practice (CiE'09)},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1007/978-3-642-03073-4},
Editor = {Ambos-Spies, K. and L\"{o}we, B. and Merkle, W.},
Eprint = {arXiv:0902.0500},
Keywords = {quantum computing; categorical quantum mechanics; graphical calculi; measurement-based quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Duncan/Graph States and the necessity of Euler Decomposition.pdf},
Pages = {167--177},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {Graph States and the necessity of {E}uler Decomposition},
Volume = {5635},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-03073-4}}
@inproceedings{Bob-Coecke:2008xr,
Abstract = {We show that Rob Spekken's toy quantum theory arises as an instance of our categorical approach to quantum axiomatics, as a (proper) subcategory of the dagger compact category FRel of finite sets and relations with the cartesian product as tensor, where observables correspond to dagger Frobenius algebras. This in particular implies that the quantum-like properties of the toy model are in fact very general category-theoretic properties. We also show the remarkable fact that we can already interpret complementary quantum observables on the two-element set FRel.},
Author = {Coecke, Bob and Edwards, Bill},
Booktitle = {Proceedings of Quantum Physics and Logic 2008},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0808.1037v1},
Journal = {Electronic Notes in theoretical Computer Science},
Keywords = {categorical quantum mechanics; toy models; alternative physical models},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Coecke/Toy quantum categories.pdf},
Number = {1},
Pages = {26-40},
Series = {Electronic Notes in Theoretical Computer Science},
Title = {Toy quantum categories},
Volume = {271},
Year = {2011},
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@article{Spekkens:2009mi,
Abstract = {Two notions of nonclassicality that have been investigated intensively are: (i) negativity, that is, the need to posit negative values when representing quantum states by quasiprobability distributions such as the Wigner representation, and (ii) contextuality, that is, the impossibility of a noncontextual hidden variable model of quantum theory (also known as the Bell-Kochen-Specker theorem). Although both of these notions were meant to characterize the conditions under which a classical explanation cannot be provided, we demonstrate that they prove inadequate to the task and we argue for a particular way of generalizing and revising them. With the refined version of each in hand, it becomes apparent that they are in fact one and the same. We also demonstrate the impossibility of noncontextuality or nonnegativity in quantum theory with a novel proof that is symmetric in its treatment of measurements and preparations.},
Author = {Spekkens, Robert W.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0710.5549v2},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum theory; alternative physical models},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Spekkens/Negativity and contextuality are equivalent notions of nonclassicality.pdf},
Number = {020401},
Title = {Negativity and contextuality are equivalent notions of nonclassicality},
Volume = {101},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.101.020401}}
@article{Barrett:2005fv,
Abstract = {I introduce a framework in which a variety of probabilistic theories can be defined, including classical and quantum theories, and many others. From two simple assumptions, a tensor product rule for combining separate systems can be derived. Certain features, usually thought of as specifically quantum, turn out to be generic in this framework, meaning that they are present in all except classical theories. These include the non-unique decomposition of a mixed state into pure states, a theorem involving disturbance of a system on measurement (suggesting that the possibility of secure key distribution is generic), and a no-cloning theorem. Two particular theories are then investigated in detail, for the sake of comparison with the classical and quantum cases. One of these includes states that can give rise to arbitrary non-signalling correlations, including the super-quantum correlations that have become known in the literature as Nonlocal Machines or Popescu-Rohrlich boxes. By investigating these correlations in the context of a theory with well-defined dynamics, I hope to make further progress with a question raised by Popescu and Rohrlich, which is, why does quantum theory not allow these strongly nonlocal correlations? The existence of such correlations forces much of the dynamics in this theory to be, in a certain sense, classical, with consequences for teleportation, cryptography and computation. I also investigate another theory in which all states are local. Finally, I raise the question of what further axiom(s) could be added to the framework in order uniquely to identify quantum theory, and hypothesize that quantum theory is optimal for computation.},
Author = {Barrett, Jonathan},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1103/PhysRevA.75.032304},
Eprint = {arXiv:quant-ph/0508211v3},
Journal = {Phys. Rev. A},
Keywords = {quantum theory; general probabilistic theories; alternative physical models},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Barrett/Information processing in generalized probabilistic theories.pdf},
Number = {032304},
Title = {Information processing in generalized probabilistic theories},
Volume = {75},
Year = {2007},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.75.032304}}
@techreport{Howard-Barnum:2006fy,
Abstract = {We prove generic versions of the no-cloning and no-broadcasting theorems, applicable to essentially {\em any} non-classical finite-dimensional probabilistic model that satisfies a no-signaling criterion. This includes quantum theory as well as models supporting ``super-quantum'' correlations that violate the Bell inequalities to a larger extent than quantum theory. The proof of our no-broadcasting theorem is significantly more natural and more self-contained than others we have seen: we show that a set of states is broadcastable if, and only if, it is contained in a simplex whose vertices are cloneable, and therefore distinguishable by a single measurement. This necessary and sufficient condition generalizes the quantum requirement that a broadcastable set of states commute.},
Author = {Barnum, Howard and Barrett, Jonathan and Leifer, Matthew and Wilce, Alexander},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0611295v1},
Institution = {Los Alamos National Laboratory},
Keywords = {quantum theory; general probabilistic theories; alternative physical models},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Barnum/Cloning and Broadcasting in Generic Probabilistic Theories.pdf},
Number = {LAUR-06-8337},
Title = {Cloning and Broadcasting in Generic Probabilistic Theories},
Year = {2006},
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@article{Howard-Barnum:2008it,
Abstract = {In a previous paper, we showed that many important quantum information-theoretic phenomena, including the no-cloning and no-broadcasting theorems, are in fact generic in all non-classical probabilistic theories. An exception is teleportation, which most such theories do not support. In this paper, we investigate which probabilistic theories, and more particularly, which composite systems, {\em do} support a teleportation protocol. We isolate a natural class of composite systems that we term {\em regular}, and establish necessary and sufficient conditions for a regular tripartite system to support a conclusive, or post-selected, teleportation protocol. We also establish a sufficient condition for deterministic teleportation that yields a large supply of theories, neither classical nor quantum, that support such a protocol.},
Author = {Barnum, Howard and Barrett, Jonathan and Leifer, Matthew and Wilce, Alexander},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0805.3553v1},
Keywords = {quantum theory; general probabilistic theories; alternative physical models},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Howard Barnum/Teleportation in General Probabilistic Theories.pdf},
Title = {Teleportation in General Probabilistic Theories},
Year = {2008},
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@incollection{Hardy:2008nx,
Abstract = {We expect a theory of Quantum Gravity to be both probabilistic and have indefinite causal structure. Indefinite causal structure poses particular problems for theory formulation since many of the core ideas used in the usual approaches to theory construction depend on having definite causal structure. For example, the notion of a state across space evolving in time requires that we have some definite causal structure so we can define a state on a space-like hypersurface. We will see that many of these problems are mitigated if we are able to formulate the theory in a "formalism local" (or F-local) fashion. A formulation of a physical theory is said to be F-local if, in making predictions for any given arbitrary space-time region, we need only refer to mathematical objects pertaining to that region. This is a desirable property both on the grounds of efficiency and since, if we have indefinite causal structure, it is not clear how to select some other space-time region on which our calculations may depend. The usual ways of formulating physical theories (the time evolving state picture, the histories approach, and the local equations approach) are not F-local. We set up a framework for probabilistic theories with indefinite causal structure. This, the causaloid framework, is F-local. We describe how Quantum Theory can be formulated in the causaloid framework (in an F-local fashion). This provides yet another formulation of Quantum Theory. This formulation, however, may be particularly relevant to the problem of finding a theory of Quantum Gravity.},
Author = {Hardy, Lucien},
Booktitle = {Philosophy of Quantum Information and Entanglement},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Bokulich, A. and Jaeger, G.},
Eprint = {arXiv:0804.0054v1},
Keywords = {quantum theory; alternative physical models; general probabilistic theories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Hardy/Formalism Locality in Quantum Theory and Quantum.pdf},
Publisher = {CUP},
Title = {Formalism Locality in Quantum Theory and Quantum Gravity},
Year = {2008},
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@inproceedings{DBLP:conf/tlca/BentonBPH93,
Author = {Benton, P. N. and Bierman, Gavin M. and de Paiva, Valeria and Hyland, Martin},
Bibsource = {DBLP, http://dblp.uni-trier.de},
Booktitle = {TLCA},
Crossref = {DBLP:conf/tlca/1993},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Benton/A Term Calculus for Intuitionistic Linear Logic.pdf},
Pages = {75-90},
Title = {A Term Calculus for Intuitionistic Linear Logic},
Year = {1993},
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@article{Blute91naturaldeduction,
Author = {Blute, R. F. and Cockett, J.R.B. and Seely, R.A.G. and Trimble, T. H.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Journal of Pure and Applied Algebra},
Keywords = {categorical logic; monoidal categories; linear logic; proof-nets},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Blute/Natural Deduction and Coherence for Weakly Distributive0.pdf},
Pages = {229--296},
Title = {Natural Deduction and Coherence for Weakly Distributive Categories},
Volume = {113},
Year = {1991},
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@article{Janet-Anders:2009lq,
Abstract = {We study the intrinsic computational power of correlations exploited in measurement-based quantum computation. By defining a general framework the meaning of the computational power of correlations is made precise. This leads to a notion of resource states for measurement-based \textit{classical} computation. Surprisingly, the Greenberger-Horne-Zeilinger and Clauser-Horne-Shimony-Holt problems emerge as optimal examples. Our work exposes an intriguing relationship between the violation of local realistic models and the computational power of entangled resource states.},
Author = {Anders, J. and Browne, D. E.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0805.1002v3},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum computing; entanglement; alternative physical models},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Janet Anders/Computational power of correlations.pdf},
Number = {050502},
Title = {Computational power of correlations},
Volume = {102},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.102.050502}}
@article{Sergei-Bravyi:2005eu,
Abstract = {We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state $|0>$, and qubit measurement in the computational basis. In addition, we allow the creation of a one-qubit ancilla in a mixed state $\rho$, which should be regarded as a parameter of the model. Our goal is to determine for which $\rho$ universal quantum computation (UQC) can be efficiently simulated. To answer this question, we construct purification protocols that consume several copies of $\rho$ and produce a single output qubit with higher polarization. The protocols allow one to increase the polarization only along certain ``magic'' directions. If the polarization of $\rho$ along a magic direction exceeds a threshold value (about 65%), the purification asymptotically yields a pure state, which we call a magic state. We show that the Clifford group operations combined with magic states preparation are sufficient for UQC. The connection of our results with the Gottesman-Knill theorem is discussed.},
Author = {Bravyi, S. and Kitaev, A},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0403025v2},
Journal = {Phys. Rev. A},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Sergei Bravyi/Universal Quantum Computation with ideal.pdf},
Number = {022316},
Title = {Universal Quantum Computation with ideal Clifford gates and noisy ancillas},
Volume = {71},
Year = {2005},
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@phdthesis{Cohen:2009vl,
Abstract = {General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language of term rewriting theory. Two general coherence theorems are obtained. The first applies to terminating and confluent rewriting 2-theories. This result is exploited to construct systematic presentations for the higher Thompson groups and the Higman-Thompson groups. The presentations are categorically interesting as they arise from higher-arity analogues of the Stasheff/Mac Lane coherence axioms, which involve phenomena not present in the classical binary axioms. The second general coherence theorem holds for 2-theories that are not necessarily confluent or terminating and is used to construct a new proof of coherence for iterated monoidal categories, which arise as categorical models of iterated loop spaces and fail to be confluent.},
Author = {Cohen, Jonathan Asher},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0904.0125v1},
Keywords = {categorical logic; rewriting; category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Cohen/Coherence for rewriting 2-theories.pdf},
School = {Australian National University},
Title = {Coherence for rewriting 2-theories},
Year = {2009},
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@article{Scott-Aaronson:2004yf,
Abstract = {The Gottesman-Knill theorem says that a stabilizer circuit -- that is, a quantum circuit consisting solely of CNOT, Hadamard, and phase gates -- can be simulated efficiently on a classical computer. This paper improves that theorem in several directions. First, by removing the need for Gaussian elimination, we make the simulation algorithm much faster at the cost of a factor-2 increase in the number of bits needed to represent a state. We have implemented the improved algorithm in a freely-available program called CHP (CNOT-Hadamard-Phase), which can handle thousands of qubits easily. Second, we show that the problem of simulating stabilizer circuits is complete for the classical complexity class ParityL, which means that stabilizer circuits are probably not even universal for classical computation. Third, we give efficient algorithms for computing the inner product between two stabilizer states, putting any n-qubit stabilizer circuit into a "canonical form" that requires at most O(n^2/log n) gates, and other useful tasks. Fourth, we extend our simulation algorithm to circuits acting on mixed states, circuits containing a limited number of non-stabilizer gates, and circuits acting on general tensor-product initial states but containing only a limited number of measurements},
Author = {Aaronson, S. and Gottesman, D},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0406196v5},
Journal = {Phys. Rev. A},
Keywords = {quantum computing; complexity},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Aaronson/Improved Simulation of Stabilizer Circuits.pdf},
Number = {052328},
Title = {Improved Simulation of Stabilizer Circuits},
Volume = {70},
Year = {2004},
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@article{AliLeu:CompByMeas:2004,
Abstract = {The ability to perform a universal set of quantum operations based solely on static resources and measurements presents us with a strikingly novel viewpoint for thinking about quantum computation and its powers. We consider the two major models for doing quantum computation by measurements that have hitherto appeared in the literature and show that they are conceptually closely related by demonstrating a systematic local mapping between them. This way we effectively unify the two models, showing that they make use of interchangeable primitives. With the tools developed for this mapping, we then construct more resource-effective methods for performing computation within both models and propose schemes for the construction of arbitrary graph states employing two-qubit measurements alone.},
Author = {Aliferis, P and Leung, D. W.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0404082v2},
Journal = {Phys. Rev. A},
Keywords = {quantum computing; measurement-based quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Panos Aliferis/Computation by measurements: a unifying picture.pdf},
Number = {062314},
Title = {Computation by measurements: a unifying picture},
Volume = {70},
Year = {2004},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.70.062314}}
@article{Daniel-Gottesman:1999nx,
Abstract = {We present a method to create a variety of interesting gates by teleporting quantum bits through special entangled states. This allows, for instance, the construction of a quantum computer based on just single qubit operations, Bell measurements, and GHZ states. We also present straightforward constructions of a wide variety of fault-tolerant quantum gates.},
Author = {Gottesman, D and Chuang, I. L.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/9908010v1},
Journal = {Nature},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Daniel Gottesman/Quantum Teleportation is a Universal Computational Primitive.pdf},
Pages = {390-393},
Title = {Quantum Teleportation is a Universal Computational Primitive},
Volume = {402},
Year = {1999},
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@article{Heunen:2009qa,
Author = {Heunen, C. and Landsman, K. and Spitters, B.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0709.4364v2},
Journal = {Communications in mathematical physics},
Keywords = {categorical quantum mechanics; categorical logic; toposes},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Heunen/A topos for algebraic quantum theory.pdf},
Title = {A topos for algebraic quantum theory},
Year = {2009},
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Bdsk-Url-1 = {http://arxiv.org/abs/0709.4364}}
@article{Doring1:2008rw,
Abstract = {This paper is the fourth in a series whose goal is to develop a fundamentally new way of building theories of physics. The motivation comes from a desire to address certain deep issues that arise in the quantum theory of gravity. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. The previous papers in this series are concerned with implementing this program for a single system. In the present paper, we turn to considering a collection of systems; in particular, we are interested in the relation between the topos representation for a composite system and the representations for its constituents. We also study this problem for the disjoint sum of two systems. Our approach to these matters is to construct a category of systems and to find a topos representation of the entire category.},
Author = {D{\"o}ring, A. and Isham, C. J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0703066},
Journal = {J. Math. Phys.},
Keywords = {entanglement; quantum gravity},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Döring/A topos foundation for theories of physics: IV. Categories.pdf},
Title = {A topos foundation for theories of physics: IV. Categories of systems},
Volume = {49},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.2883826}}
@article{Doring:2008kl,
Abstract = {This paper is the third in a series whose goal is to develop a fundamentally new way of viewing theories of physics. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. In Paper II, we studied the topos representations of the propositional language (S) for the case of quantum theory, and in the present paper we do the same thing for the, more extensive, local language (S). One of the main achievements is to find a topos representation for self-adjoint operators. This involves showing that, for any physical quantity A, there is an arrow o(A):, where is the quantity-value object for this theory. The construction of o({\^A}) is an extension of the daseinisation of projection operators that was discussed in Paper II. The object is a monoid object only in the topos, =Sets, of the theory, and to enhance the applicability of the formalism, we apply to a topos analog of the Grothendieck extension of a monoid to a group. The resulting object, k(), is an abelian group object in . We also discuss another candidate, , for the quantity-value object. In this presheaf, both inner and outer daseinisations are used in a symmetric way. Finally, there is a brief discussion of the role of unitary operators in the quantum topos scheme},
Author = {D{\"o}ring, A. and Isham, C. J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0703064},
Journal = {J. Math. Phys},
Keywords = {quantum theory; toposes; category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Döring/A topos foundation for theories of physics: III..pdf},
Title = {A topos foundation for theories of physics: III. The representation of physical quantities with arrows o(A):},
Volume = {49},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.2883777}}
@article{A.-Doering:2007dk,
Abstract = {This paper is the second in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. In this paper, we study in depth the topos representation of the propositional language, PL(S), for the case of quantum theory. In doing so, we make a direct link with, and clarify, the earlier work on applying topos theory to quantum physics. The key step is a process we term `daseinisation' by which a projection operator is mapped to a sub-object of the spectral presheaf--the topos quantum analogue of a classical state space. In the second part of the paper we change gear with the introduction of the more sophisticated local language L(S). From this point forward, throughout the rest of the series of papers, our attention will be devoted almost entirely to this language. In the present paper, we use L(S) to study `truth objects' in the topos. These are objects in the topos that play the role of states: a necessary development as the spectral presheaf has no global elements, and hence there are no microstates in the sense of classical physics. Truth objects therefore play a crucial role in our formalism.},
Author = {Doering, A. and Isham, C. J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0703062v1},
Journal = {J. Math. Phys},
Keywords = {quantum theory; toposes; category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Doering/A Topos Foundation for Theories of Physics: II. Daseinisation.pdf},
Title = {A Topos Foundation for Theories of Physics: II. Daseinisation and the Liberation of Quantum Theory},
Volume = {49},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.2883740}}
@article{A.-Doering:2007fu,
Abstract = {This paper is the first in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. In this paper we discuss two different types of language that can be attached to a system, S. The first is a propositional language, PL(S); the second is a higher-order, typed language L(S). Both languages provide deductive systems with an intuitionistic logic. The reason for introducing PL(S) is that, as shown in paper II of the series, it is the easiest way of understanding, and expanding on, the earlier work on topos theory and quantum physics. However, the main thrust of our programme utilises the more powerful language L(S) and its representation in an appropriate topos.},
Author = {Doering, A. and Isham, C. J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0703060v1},
Journal = {J. Math. Phys},
Keywords = {quantum theory; toposes; category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Doering/A Topos Foundation for Theories of Physics: I. Formal.pdf},
Title = {A Topos Foundation for Theories of Physics: I. Formal Languages for Physics},
Volume = {49},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.2883740}}
@incollection{Bob-Coecke:2008ty,
Abstract = {This paper contains two new results: 1. We amend the notion of abstract basis in a dagger symmetric monoidal category, as well as its corresponding graphical representation, in order to accommodate non-self-dual dagger compact structures; this is crucial for obtaining a `planar' diagrammatical representation of the induced dagger compact structure as well as for representing many complementary bases within one diagrammatic calculus. 2. We (crucially) rely on these basis structures in a purely diagrammatic derivation of the `quantum state transfer protocol'; this derivation provides interesting insights in the distinct structural resources required for state-transfer and teleportation as models of quantum computing.},
Author = {Coecke, B. and Paquette, E. O. and Perdrix, S.},
Booktitle = {Proceedings of Mathematical Foundations of Programming Semantics XXIV},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory; quantum computing; quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Bob Coecke/Bases in diagrammatic quantum protocols.pdf},
Pages = {131-152},
Publisher = {Elsevier},
Series = {Electronic Notes in Theoretical Computer Science},
Title = {Bases in diagrammatic quantum protocols},
Volume = {218},
Year = {2008},
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@article{Lack:2004sf,
Abstract = {A PROP is a way of encoding structure borne by an object of a symmetric monoidal category. We describe a notion of distributive law for PROPs, based on Beck's distributive laws for monads. A distributive law between PROPs allows them to be composed, and an algebra for the composite PROP consists of a single object with an algebra structure for each of the original PROPs, subject to compatibility conditions encoded by the distributive law. An example is the PROP for bialgebras, which is a composite of the PROP for coalgebras and that for algebras.},
Author = {Lack, Stephen},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {http://www.tac.mta.ca/tac/volumes/13/9/13-09abs.html},
Journal = {Theory and Applications of Categories},
Keywords = {category theory; monoidal categories; graphical calculi},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Lack/Composing PROPs.pdf},
Number = {9},
Pages = {147-163},
Title = {Composing {PROP}s},
Volume = {13},
Year = {2004},
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@inproceedings{E.:2001qq,
Author = {Haghverdi, E.},
Booktitle = {Proceedings of TLCA'01},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic; monoidal categories; categorical logic},
Pages = {197-216},
Publisher = {Springer},
Series = {LNCS},
Title = {Partially Additive Categories and Fully Complete Models of Linear Logic},
Volume = {2044},
Year = {2001}}
@misc{PaulsonNipkow:isabelle,
Author = {Paulson, Lawrence and Nipkow, Tobias},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {interactive theorem proving; tools},
Title = {Isabelle},
Bdsk-Url-1 = {http://isabelle.in.tum.de/}}
@article{Lucas-Dixon:2009yq,
Abstract = {Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning about such graphs and develop this into a generic proof system with a fixed logical kernel for equational reasoning about compact closed categories. Automating this reasoning process is motivated by the slow and error prone nature of manual graph manipulation. A salient feature of our system is that it provides a formal and declarative account of derived results that can include `ellipses'-style notation. We illustrate the framework by instantiating it for a graphical language of quantum computation and show how this can be used to perform symbolic computation.},
Author = {Dixon, Lucas and Duncan, Ross},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1007/s10472-009-9141-x},
Eprint = {arXiv:0902.0514},
Journal = {Annals of Mathematics and Artificial Intelligence},
Keywords = {rewriting; categorical quantum mechanics; compact closed categories; rewriting; graphical calculi},
Number = {1},
Pages = {23-42},
Title = {Graphical Reasoning in Compact Closed Categories for Quantum Computation},
Volume = {56},
Year = {2009},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10472-009-9141-x}}
@mastersthesis{Kissinger:2008kx,
Author = {Kissinger, Aleks},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {categorical quantum mechanics; graphical calculi; rewriting; monoidal categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Kissinger/Graph rewrite systems for complementary classical.pdf},
School = {Oxford University},
Title = {Graph rewrite systems for complementary classical structures in $\dag$-symmetric monoidal categories.},
Year = {2008},
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@inproceedings{HDERNB06-survey,
Author = {Hein, M. and D\"ur, W. and Eisert, J. and Raussendorf, R. and Van den Nest, M. and Briegel, H. J.},
Booktitle = {Proceedings of the International School of Physics ``Enrico Fermi'' on ``Quantum Computers, Algorithms and Chaos''},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-09-08 16:30:27 +0000},
Keywords = {surveys; entanglement; measurement-based quantum computing; quantum computing},
Title = {Entanglement in graph states and its applications.},
Year = {2005}}
@article{VdN04,
Author = {Van den Nest, M. and Dehaene, J. and {De Moor}, B.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Physical Review A},
Keywords = {quantum computing; entanglement; measurement-based quantum computing},
Pages = {022316},
Title = {Graphical description of the action of local Clifford transformations on graph states},
Volume = {69},
Year = {2004},
Bdsk-Url-1 = {http://www.citebase.org/abstract?id=oai:arXiv.org:quant-ph/0308151}}
@article{PavlovicD:MSCS08,
Author = {Coecke, B. and Pavlovic, D. and Vicary, J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-10-10 08:37:38 +0000},
Doi = {10.1017/S0960129512000047},
Eprint = {arxiv:0810.0812},
Journal = {Math. Structures in Comp. Sci.},
Keywords = {categorical quantum mechanics; monoidal categories; category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Coecke/A new description of orthogonal bases.pdf},
Number = {3},
Pages = {555-567},
Title = {A new description of orthogonal bases},
Volume = {23},
Year = {2013},
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@incollection{Howard:1980kb,
Author = {Howard, W. A.},
Booktitle = {To H. B. Curry, Essays on Combinatory Logic, Lambda Calculus and Formalism},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Hindley, J. R. and Seldin, J. P.},
Keywords = {lambda calculus; proof theory; logic},
Pages = {479--490},
Publisher = {Academic Press},
Title = {The formul{\ae}-as-types notion of construction},
Year = {1980}}
@techreport{Cardone:2006vl,
Author = {Cardone, F. and Hindley, J. R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Institution = {Swansea University Mathematics Department},
Keywords = {logic; surveys; lambda calculus; combinatory logic},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Cardone/History of Lambda-calculus and Combinatory Logic.pdf},
Number = {MRRS-05-06},
Title = {History of Lambda-calculus and Combinatory Logic},
Year = {2006},
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@article{Dosen:2003yq,
Author = {Do\v{s}en, Kosta},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {The Bulletin of Symbolic Logic},
Keywords = {surveys; proof theory; categorical logic},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Dosen/Identity of Proofs Based on Normalization and Generality.pdf},
Month = {December},
Number = {4},
Pages = {477-503},
Read = {Yes},
Title = {Identity of Proofs Based on Normalization and Generality},
Volume = {9},
Year = {2003},
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@article{Macintyre:2003kx,
Author = {Macintyre, Angus},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {The Bulletin of Symbolic Logic},
Keywords = {model theory; surveys},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Macintyre/Model Theory: Geometrical and Set-theoretic Aspects.pdf},
Month = {June},
Number = {2},
Pages = {197-212},
Read = {Yes},
Title = {Model Theory: Geometrical and Set-theoretic Aspects and Prospects},
Volume = {9},
Year = {2003},
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@inproceedings{Dixon:2008ys,
Abstract = {Graph-based formalisms of quantum computation provide an abstract and symbolic way to represent and simulate computations. However, manual manipulation of such graphs is slow and error prone. We present a formalism, based on compact closed categories, that supports mechanised reasoning about such graphs. This gives a compositional account of graph rewriting that preserves the underlying categorical semantics. Using this representation, we describe a generic system with a fixed logical kernel that supports reasoning about models of compact closed category. A salient feature of the system is that it provides a formal and declarative account of derived results that can include `ellipses'-style notation. We illustrate the framework by instantiating it for a graphical language of quantum computation and show how this can be used to perform symbolic computation},
Author = {Dixon, Lucas and Duncan, Ross},
Booktitle = {Intelligent Computer Mathematics, 9th International Conference, AISC 2008, 15th Symposium, Calculemus 2008, 7th International Conference, MKM 2008, Birmingham, UK, July 28 - August 1, 2008. Proceedings},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Autexier, Serge and Campbell, John and Rubio, Julio and Sorge, Volker and Suzuki, Masakazu and Wiedijk, Freek},
Keywords = {rewriting; quantum computing; categorical logic; interactive theorem proving; graphical calculi},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Dixon/Extending Graphical Representations for Compact Closed.pdf},
Pages = {77-92},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {Extending Graphical Representations for Compact Closed Categories with Applications to Symbolic Quantum Computation},
Volume = {5144},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-540-85110-3_8}}
@inproceedings{Coecke:2008nx,
Abstract = {We formalise the constructive content of an essential feature of quantum mechanics: the interaction of complementary quantum observables, and information flow mediated by them. Using a general categorical formulation, we show that pairs of mutually unbiased quantum observables form bialgebra-like structures. We also provide an abstract account on the quantum data encoded in complex phases, and prove a normal form theorem for it. Together these enable us to describe all observables of finite dimensional Hilbert space quantum mechanics. The resulting equations suffice to perform computations with elementary quantum gates, translate between distinct quantum computational models, establish the equivalence of entangled quantum states, and simulate quantum algorithms such as the quantum Fourier transform. All these computations moreover happen within an intuitive diagrammatic calculus.},
Author = {Coecke, B. and Duncan, R.},
Booktitle = {Automata, Languages and Programming, 35th International Colloquium, ICALP 2008, Reykjavik, Iceland, July 7-11, 2008, Proceedings, Part II},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Aceto, L. and Damg{\aa}rd, I. and Goldberg, L. A. and Halld{\'o}rsson, M. M. and Ing{\'o}lfsd{\'o}ttir, A and Walukiewic, I.},
Keywords = {categorical quantum mechanics; quantum computing;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Coecke/Interacting Quantum Observables.pdf},
Pages = {298-310},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {Interacting Quantum Observables},
Volume = {5126},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-540-70583-3_25}}
@unpublished{Tomasz-Paterek:2008lq,
Abstract = {Mutually unbiased bases encapsulate the concept of complementarity in the formalism of quantum theory. Although this concept is at the heart of quantum mechanics, the number of these bases is unknown except for systems of dimension being a power of a prime. We develop the relation between this physical problem and the mathematical problem of finding the number of mutually orthogonal Latin squares. We use already existing knowledge about the squares to derive in a simple way all known results about the unbiased bases, find the lower bound on their number, and disprove the existence of certain forms of the bases in dimensions different than power of a prime. Our results can be used to construct hidden-variable models which efficiently simulate results of complementary measurements on quantum systems with arbitrary dimension.},
Author = {Paterek, Tomasz and Dakic, Borivoje and Brukner, Caslav},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0804.2193v1 [quant-ph]},
Keywords = {quantum theory, mutually unbiased bases},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Tomasz Paterek/Mutually Unbiased Bases and Orthogonal Latin.pdf},
Note = {Superceded by PRA 79 (2009) by same authors},
Title = {Mutually Unbiased Bases and Orthogonal Latin Squares},
Year = {2008},
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@article{Timpson:2008eu,
Abstract = {The Bayesian approach to quantum mechanics of Caves, Fuchs and Schack is presented. Its conjunction of realism about physics along with anti-realism about much of the structure of quantum theory is elaborated; and the position defended from common objections: that it is solipsist; that it is too instrumentalist; that it cannot deal with Wigner's friend scenarios. Three more substantive problems are raised: Can a reasonable ontology be found for the approach? Can it account for explanation in quantum theory? Are subjective probabilities on their own adequate in the quantum domain? The first question is answered in the affirmative, drawing on elements from Nancy Cartwright's philosophy of science. The second two are not: it is argued that these present outstanding difficulties for the project. A quantum Bayesian version of Moore's paradox is developed to illustrate difficulties with the subjectivist account of pure state assignments.},
Author = {Timpson, Christopher G.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0804.2047v1 [quant-ph]},
Journal = {Studies in History and Philosophy of Modern Physics},
Keywords = {quantum theory; alternative physical models;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Timpson/Quantum Bayesianism: A Study.pdf},
Title = {Quantum Bayesianism: A Study},
Year = {2008},
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@article{Bruno-Bellomo:2007kx,
Abstract = {A procedure that allows to obtain the dynamics of $N$ independent bodies each locally interacting with its own reservoir is presented. It relies on the knowledge of single body dynamics and it is valid for any form of environment noise. It is then applied to the study of non-Markovian dynamics of two independent qubits, each locally interacting with a zero temperature reservoir. It is shown that, although no interaction is present or mediated between the qubits, there is a revival of their entanglement, after a finite period of time of its complete disappearance.},
Author = {Bellomo, Bruno and Franco, Rosario Lo and Compagno, Giuseppe},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0804.2377v1},
Journal = {Physical Review Letters},
Keywords = {quantum computing, entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Bruno Bellomo/Non-Markovian effects on the dynamics of entanglement.pdf},
Title = {Non-Markovian effects on the dynamics of entanglement},
Volume = {99},
Year = {2007},
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@unpublished{Vicary:2007ek,
Abstract = {This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction of categories, that encodes the raising and lowering operators into a commutative comonoid. The formulation is an entirely general one in which Hilbert spaces play no special role. Generalised coherent states arise through the hom-set isomorphisms defining the adjunction, and we prove that they are eigenstates of the lowering operators. Surprisingly, generalised exponentials also emerge naturally in this setting, and we demonstrate that coherent states are produced by the exponential of a raising morphism acting on the zero-particle state. Finally, we examine all of these constructions in a suitable category of Hilbert spaces, and find that they reproduce the conventional mathematical structures.},
Author = {Vicary, Jamie},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0706.0711v2},
Keywords = {categorical quantum mechanics},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Vicary/A categorical framework for the quantum harmonic oscillator.pdf},
Title = {A categorical framework for the quantum harmonic oscillator},
Year = {2007},
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@article{Grover:1997qc,
Abstract = {This paper shows that a quantum mechanical algorithm that can query information relating to multiple items of the database can search a database for a unique item satisfying a given condition, in a single query [a query is defined as any question to the database to which the database has to return a (YES/NO answer]. A classical algorithm will be limited to the information theoretic bound of at least log_2 N queries, which it would achieve by using a binary search.},
Author = {Grover, Lov K.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Grover/Quantum Computers Can Search Arbitrarily Large.pdf},
Number = {23},
Pages = {4709-4712},
Title = {Quantum Computers Can Search Arbitrarily Large Databases by a Single Query},
Volume = {79},
Year = {1997},
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@article{J.-K.-Korbicz:2008wq,
Abstract = {We describe quantum mechanical entanglement in terms of compact quantum groups. We prove an analog of positivity of partial transpose (PPT) criterion and formulate a Horodecki-type Theorem.},
Author = {Korbicz, J. K. and Wehr, J. and Lewenstein, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0802.1492v1},
Keywords = {entanglement; quantum theory; quantum computing; algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/J. K. Korbicz/Entanglement and Quantum Groups.pdf},
Month = {Feb},
Title = {Entanglement and Quantum Groups},
Year = {2008},
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@article{R.-Hubener:2008lr,
Abstract = {We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underly the density-matrix renormalization group approach by combining them with weighted graph states. States within this class may (i) possess arbitrarily long-ranged two-point correlations, (ii) exhibit an arbitrary degree of block entanglement entropy up to a volume law, (iii) may be taken translationally invariant, while at the same time (iv) local properties and two-point correlations can be computed efficiently. This new variational class of states can be thought of as being prepared from matrix product states, followed by commuting unitaries on arbitrary constituents, hence truly generalizing both matrix product and weighted graph states. We use this class of states to formulate a renormalization algorithm with graph enhancement (RAGE) and present numerical examples demonstrating that improvements over density-matrix renormalization group simulations can be achieved in the simulation of ground states and quantum algorithms. Further generalizations, e.g., to higher spatial dimensions, are outlined.},
Author = {H{\"u}bener, R. and Kruszynska, C. and Hartmann, L. and D{\"u}r, W. and Verstraete, F. and Eisert, J. and Plenio, M.B.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0802.1211v1},
Keywords = {quantum computing; quantum many-body; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Hübener/Renormalization algorithm with graph enhancement.pdf},
Month = {Feb},
Title = {Renormalization algorithm with graph enhancement},
Year = {2008},
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@article{Svetlichny:2007kk,
Abstract = {The Feynman integral can be seen as an attempt to relate, under certain circumstances, the quantum-information-theoretic separateness of mutually unbiased bases to causal proximity of the measuring processes.},
Author = {Svetlichny, George},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0708.3079v3},
Keywords = {quantum theory; mutually unbiased bases},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Svetlichny/Feynman's Integral is About Mutually Unbiased.pdf},
Month = {Aug},
Title = {Feynman's Integral is About Mutually Unbiased Bases},
Year = {2007},
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@article{Yoran:2008ud,
Abstract = {We show a similarity between two different classical simulation methods for measurement based quantum computation -- one relying on a low entanglement (tree tensor network) representation of the computer's state, and the other a tensor contraction method based on the topology of the graph state. We use this similarity to show that any quantum circuit that can be efficiently simulated via tensor contraction cannot produce much entanglement.},
Author = {Yoran, Nadav},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0802.1156v1},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Yoran/Efficiently contractable quantum circuits cannot.pdf},
Month = {Feb},
Title = {Efficiently contractable quantum circuits cannot produce much entanglement},
Year = {2008},
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@article{G.-H.-E.-Duchamp-LIPN2008Hopf-Algebras-i,
Abstract = {This tutorial is intended to give an accessible introduction to Hopf algebras. The mathematical context is that of representation theory, and we also illustrate the structures with examples taken from combinatorics and quantum physics, showing that in this latter case the axioms of Hopf algebra arise naturally. The text contains many exercises, some taken from physics, aimed at expanding and exemplifying the concepts introduced.},
Author = {Duchamp, G. H. E. and Blasiak, P. and Horzela, A. and Penson, K. A. and Solomon, A. I.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0802.0249v1},
Keywords = {surveys; category theory; quantum theory; monoidal categories; algebra},
Month = {Feb},
Title = {Hopf Algebras in General and in Combinatorial Physics: a practical introduction},
Year = {2008}}
@unpublished{Klappenecker2003Constructions-o,
Author = {Klappenecker, A. and R\"{o}ttler, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {quant-ph/0309120},
Keywords = {mutually unbiased bases; quantum computing; quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Klappenecker/Constructions of Mutually Unbiased Bases.pdf},
Month = {September},
Note = {arxiv preprint.},
Title = {Constructions of Mutually Unbiased Bases},
Year = {2003},
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@article{Maassen1988Generalized-ent,
Abstract = {A new class of uncertainty relations is derived for pairs of observables in a finite-dimensional Hilbert space which do not have any common eigenvector. This class contains an ``entropic'' uncertainty relation which improves a previous result of Deutsch and confirms a recent conjecture by Kraus. Some comments are made on the extension of these relations to the case where the Hilbert space is infinite dimensional.},
Author = {Maassen, H. and Uffink, J. B. M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Dc:Creator = {J. B. M. Uffink},
Dc:Date = {1988-03-21},
Dc:Format = {text/html},
Dc:Identifier = {10.1103/PhysRevLett.60.1103},
Dc:Source = {Phys. Rev. Lett.},
Dc:Type = {article},
Journal = {Phys. Rev. Lett.},
Keywords = {mutually unbiased bases, quantum computing, quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Maassen/Generalized entropic uncertainty relations.pdf},
Month = {March},
Number = {12},
Pages = {1103 - 1106},
Prism:Category = {abstract},
Prism:Endingpage = {1106},
Prism:Issueidentifier = {12},
Prism:Publicationdate = {1988-03-21},
Prism:Publicationname = {Physical Review Letters},
Prism:Section = {General Physics},
Prism:Startingpage = {1103},
Prism:Volume = {60},
Title = {Generalized entropic uncertainty relations},
Volume = {60},
Year = {1988},
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Bdsk-Url-1 = {http://link.aps.org/abstract/PRL/v60/p1103},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.60.1103}}
@article{Kraus1987Complementary-o,
Abstract = {Two observables A and B of an n-level system (i.e., a quantum system with n-dimensional state space) are called complementary, if knowledge of the measured value of A implies maximal uncertainty of the measured value of B, and vice versa. Such observables exist for all n, but no classification (up to equivalence) of all possible pairs of complementary observables is known except for n<=4. Complementary observables are conjectured to satisfy an ``entropic'' uncertainty relation of the strongest possible form. This relation has been verified for n<=4 by explicit calculations. A recent attempt of substantiating the widespread interpretation of uncertainty relations in terms of mutual disturbances between measurements is criticized.},
Author = {Kraus, K.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Physics Review D},
Keywords = {mutually unbiased bases, quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Kraus/Complementary observables and uncertainty relations.pdf},
Month = {May},
Number = {10},
Pages = {3070 - 3075},
Title = {Complementary observables and uncertainty relations},
Volume = {35},
Year = {1987},
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Bdsk-Url-1 = {http://link.aps.org/abstract/PRD/v35/p3070},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevD.35.3070}}
@article{Ivanovic1981Geometrical-des,
Abstract = {Under the assumption that every quantal measurement may give data about the post-measurement state of the inspected ensemble, the problem of the state determination is reconsidered. It is shown that orthogonal decomposition of the set of complex, n x n, Hermitian matrices into the commutative subsets allows operators to be found such that post-measurement information on these observables allows a partial (in same cases total) determination of the pre-measurement state to be effected. },
Author = {Ivanovic, I. D.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Journal of Physics A : mathematical and general},
Keywords = {mutually unbiased bases, quantum computing, quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Ivanovic/Geometrical descrption of quantal state determination.pdf},
Pages = {3241-3245},
Title = {Geometrical descrption of quantal state determination},
Volume = {14},
Year = {1981},
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@article{Burns1989Maximal-Order-A,
Author = {Burns, J. M. and Goldsmith, B.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Bulletin of the London Mathematical Society},
Keywords = {algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Burns/Maximal Order Abelian Subgroups of Symmetric.pdf},
Pages = {70-72},
Title = {Maximal Order Abelian Subgroups of Symmetric Groups},
Volume = {21},
Year = {1989},
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@article{Wooters1989Optimal-State-D,
Abstract = {For quantum systems having a linite number N of orthogonal states, we investigate a particular relation among different measurements, called ``mutual unbiasedness,'' which we show plays a special role in the problem of state determination. We define two bases {Iv,)} and { Iw,) } to be mutually unbiased if all inner products across their elements have the same magnitude: 1 (u, 1 w,) 1 = l/fi f or all i, j. Two non-degenerate measurements are defined to be mutually unbiased if the bases comprising their eigenstates are mutually unbiased. We show that if one can find N + 1 mutually unbiased bases for a complex vector space of N dimen- sions, then the measurements corresponding to these bases provide an optimal means of deter- mining the density matrix of an ensemble of systems having N orthogonal states, in the sense that the effects of statistical error are minimized. We show further that the number of mutually unbiased bases one may find for a given N is at most N+ 1. Finally, we show that N + 1 mutually unbiased bases do exist whenever N is a power of a prime, and we construct such bases explicitly. },
Author = {Wootters, W. K. and Fields, B. D.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Annals of Physics},
Keywords = {quantum theory, mutually unbiased bases, quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Wooters/Optimal State Determination by Mutually Unbiased.pdf},
Pages = {363-381},
Title = {Optimal State Determination by Mutually Unbiased Measurements},
Volume = {191},
Year = {1989},
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@unpublished{Duncan2003Quantum-Entangl,
Author = {Duncan, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic; quantum computing; proof-nets},
Note = {Oxford University Computing Laboratory, PRS Transfer Report},
Title = {Quantum Entanglement and Multiplicative Linear Logic},
Year = {2003}}
@article{Browne2005Efficient-Linea,
Author = {Browne, D. E. and Rudolph, T.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum computing},
Title = {Efficient Linear Optics Quantum Computing},
Year = {2005}}
@article{BeaudrapPei-2008,
Acmid = {2011777},
Address = {Paramus, NJ},
Author = {de Beaudrap, Niel and Pei, Martin},
Issn = {1533-7146},
Issue_Date = {May 2008},
Journal = {Quantum Info. Comput.},
Keywords = {flows, measurement-based quantum computing},
Month = may,
Number = {5},
Numpages = {8},
Pages = {430--437},
Publisher = {Rinton Press, Incorporated},
Title = {An Extremal Result for Geometries in the One-way Measurement Model},
Volume = {8},
Year = {2008}}
@unpublished{Beaudrap2006Characterizing-,
Author = {de Beaudrap, Niel},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {quant-ph/0603072v4},
Keywords = {quantum computing; ; measurement-based quantum computing},
Note = {arxiv:quant-ph/0603072v4},
Title = {A complete algorithm to find flows in the one-way measurement model},
Year = {2006}}
@inproceedings{Brown1994Categories-alle,
Author = {Brown, Carolyn and Hutton, Graham},
Booktitle = {Proceedings of the 10th Annual IEEE symposium on Logic in Computer Science},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory; programming language; graphical calculi},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Brown/Categories, allegories, and circuit design.pdf},
Organization = {IEEE},
Publisher = {IEEE Computer Society Press},
Title = {Categories, allegories, and circuit design},
Year = {1994},
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Bdsk-Url-1 = {http://www.cs.nott.ac.uk/~gmh/bib.html#allegories}}
@article{Wootters1982A-single-quantu,
Author = {Wootters, W. and Zurek, W.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Nature},
Keywords = {quantum theory},
Pages = {802--803},
Title = {A single quantum cannot be cloned},
Volume = {299},
Year = {1982}}
@incollection{Penrose1971Applications-of,
Author = {Penrose, R.},
Booktitle = {Combinatorial Mathematics and its Applications},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum theory; graphical calculi},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Penrose/Applications of negative dimensional tensors.pdf},
Pages = {221-244},
Publisher = {Academic Press},
Title = {Applications of negative dimensional tensors},
Year = {1971},
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@article{Swinger1960Unitary-Operato,
Author = {Schwinger, J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Proc. Nat. Acad. Sci. U.S.A.},
Keywords = {quantum theory; mutually unbiased bases},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Swinger/Unitary Operator Bases.pdf},
Pages = {570--579},
Title = {Unitary Operator Bases},
Volume = {46},
Year = {1960},
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@article{D.E.-Browne2007Generalized-Flo,
Abstract = {We extend the notion of quantum information flow defined by Danos and Kashefi (2006 Phys. Rev. A 74 052310) for the one-way model (Raussendorf and Briegel 2001 Phys. Rev. Lett. 86 910) and present a necessary and sufficient condition for the stepwise uniformly deterministic computation in this model. The generalized flow also applied in the extended model with measurements in the (X, Y), (X, Z) and (Y, Z) planes. We apply both measurement calculus and the stabiliser formalism to derive our main theorem which for the first time gives a full characterization of the stepwise uniformly deterministic computation in the one-way model. We present several examples to show how our result improves over the traditional notion of flow, such as geometries (entanglement graph with input and output) with no flow but having generalized flow and we discuss how they lead to an optimal implementation of the unitaries. More importantly one can also obtain a better quantum computation depth with the generalized flow rather than with flow. We believe our characterization result is particularly valuable for the study of the algorithms and complexity in the one-way model.},
Author = {Browne, Dan E. and Kashefi, Elham and Mhalla, Mehdi and Perdrix, Simon},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1088/1367-2630/9/8/250},
Eprint = {arXiv:quant-ph/0702212v1},
Journal = {New J. Phys},
Keywords = {quantum computing; entanglement; measurement-based quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Browne/Generalized Flow and Determinism in Measurement-based Quantum.pdf},
Month = {August},
Number = {250},
Title = {Generalized Flow and Determinism in Measurement-based Quantum Computation},
Volume = {9},
Year = {2007},
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Bdsk-Url-1 = {http://arxiv.org/abs/quant-ph/0702212},
Bdsk-Url-2 = {http://dx.doi.org/10.1088/1367-2630/9/8/250}}
@article{Anne-Broadbent2007Parallelizing-Q,
Author = {Broadbent, A. and Kashefi, E.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0704.1736v1},
Keywords = {complexity, measurement-based quantum computing; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Broadbent/Parallelizing Quantum Circuits.pdf},
Month = {April},
Title = {Parallelizing Quantum Circuits},
Year = {2007},
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Bdsk-Url-1 = {http://arxiv.org/abs/0704.1736}}
@article{DHondt2005Computational-Power-GHZ,
Abstract = {It is well understood that the use of quantum entanglement significantly enhances the computational power of systems. Much of the attention has focused on Bell states and their multipartite generalizations. However, in the multipartite case it is known that there are several inequivalent classes of states, such as those represented by the W-state and the GHZ-state. Our main contribution is a demonstration of the special computational power of these states in the context of paradigmatic problems from classical distributed computing. Concretely, we show that the W-state is the only pure state that can be used to exactly solve the problem of leader election in anonymous quantum networks. Similarly we show that the GHZ-state is the only one that can be used to solve the problem of distributed consensus when no classical post-processing is considered. These results generalize to a family of W- and GHZ-like states. At the heart of the proofs of these impossibility results lie symmetry arguments.},
Author = {D'Hondt, E. and Panangaden, P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {quant-ph/0412177},
Journal = {Journ. Quantum Inf. and Comp},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Ellie D'Hondt/The Computational Power of the W and GHZ states.pdf},
Number = {2},
Pages = {173-183},
Title = {The Computational Power of the {W} and {GHZ} states},
Volume = {6},
Year = {2005},
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@article{Ingemar-Bengtsson2006Mubs-and-Hadama,
Abstract = {We report on a search for mutually unbiased bases (MUBs) in 6 dimensions. We find only triplets of MUBs, and thus do not come close to the theoretical upper bound 7. However, we point out that the natural habitat for sets of MUBs is the set of all complex Hadamard matrices of the given order, and we introduce a natural notion of distance between bases in Hilbert space. This allows us to draw a detailed map of where in the landscape the MUB triplets are situated. We use available tools, such as the theory of the discrete Fourier transform, to organise our results. Finally we present some evidence for the conjecture that there exists a four dimensional family of complex Hadamard matrices of order 6. If this conjecture is true the landscape in which one may search for MUBs is much larger than previously thought.},
Author = {Bengtsson, A and Bruzda, W. and Ericsson, A. and Larsson, J.-A. and Tadej, W. and Zyczkowski, K.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {quant-ph/0610161},
Keywords = {quantum computing; mutually unbiased bases},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Ingemar Bengtsson/Mubs and Hadamards of Order Six.pdf},
Title = {Mubs and Hadamards of Order Six},
Year = {2006},
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@article{Sergey-Bravyi2006On-measurement-,
Abstract = {We study measurement-based quantum computation (MQC) using as quantum resource the planar code state on a two-dimensional square lattice (planar analogue of the toric code). It is shown that MQC with the planar code state can be efficiently simulated on a classical computer if at each step of MQC the sets of measured and unmeasured qubits correspond to connected subsets of the lattice.},
Author = {Bravyi, S. and Raussendorf, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {quant-ph/0610162},
Keywords = {quantum computing; measurement-based quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Bravyi/On measurement-based quantum computation with the toric.pdf},
Title = {On measurement-based quantum computation with the toric code states},
Year = {2006},
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@article{Yong-Zhang-12006New-Quantum-Alg,
Abstract = {The antisymmetric solution of eight-vertex models called the Bell matrix becomes interesting in quantum information phenomena because it can generate all Bell states from product states. In this paper, we obtain a new quantum algebra through the FRT construction of the Bell matrix. In its four dimensional representations via the coproduct of its two dimensional representations, we find algebraic structures including a composition series and a direct sum of its two dimensional representations to characterize this quantum algebra. We also present the quantum algebra using the FRT construction of Yang--Baxterization of the Bell matrix.},
Author = {Zhang, Y. and Jing, N. and Ge, M-L},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {math-ph/0610036},
Keywords = {quantum theory; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Zhang/New Quantum Algebras Associated With Bell.pdf},
Month = {Oct},
Title = {New Quantum Algebras Associated With Bell States},
Year = {2006},
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@article{John-Conway2006On-Adlers-Conwa,
Abstract = {We respond to Stephen Adler's comments on our paper "The Free Will Theorem",and add some further observations.},
Author = {Conway, J. and Kochen, S.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {quant-ph/0610147},
Keywords = {quantum theory; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Conway/On Adler's "Conway-Kochen Twin Argument".pdf},
Month = {Oct},
Title = {On Adler's "Conway-Kochen Twin Argument"},
Year = {2006},
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@article{Zhang2006Teleportation-B,
Abstract = {We explore algebraic and topological structures underlying the quantum teleportation phenomena by applying the braid group and Temperley--Lieb algebra. We realize the braid teleportation configuration, teleportation swapping and virtual braid representation in the standard description of the teleportation. We devise diagrammatic rules for quantum circuits involving maximally entangled states and apply them to three sorts of descriptions of the teleportation: the transfer operator, quantum measurements and characteristic equations, and further propose the Temperley--Lieb algebra under local unitary transformations to be a mathematical structure underlying the teleportation. We compare our diagrammatical approach with two known recipes to the quantum information flow: the teleportation topology and strongly compact closed category, in order to explain our diagrammatic rules to be a natural diagrammatic language for the teleportation.},
Author = {Zhang, Y.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {quant-ph/0610148},
Journal = {Journal of Physics A : mathematical and general},
Keywords = {monoidal categories, categorical quantum mechanics},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Zhang/Teleportation, Braid Group and Temperley--Lieb Algebra.pdf},
Pages = {11599-11622},
Title = {Teleportation, Braid Group and Temperley--Lieb Algebra},
Volume = {39},
Year = {2006},
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@article{Makkai2005The-Word-Proble,
Author = {Makkai, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory; categorical logic;},
Title = {The Word Problem for Computads},
Year = {2005},
Bdsk-Url-1 = {http://www.math.mcgill.ca/makkai}}
@misc{Batanin2002Computads-and-s,
Abstract = {For a given $\omega$-operad $A$ on globular sets we introduce a sequence of symmetric operads on $Set$ called slices of $A$ and show how the connected limit preserving properties of slices are related to the property of the category of $n$-computads of $A$ being a presheaf topos.},
Author = {Batanin, M.A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {math.CT/0209035},
Keywords = {category theory;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Batanin/Computads and slices of operads.pdf},
Title = {Computads and slices of operads},
Year = {2002},
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@article{John-C.-Baez1995Higher-dimensio,
Abstract = {The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of n-category suited for this purpose, and outline a program in which n-dimensional TQFTs are to be described as n-category representations. First we describe a "suspension" operation on n-categories, and hypothesize that the k-fold suspension of a weak n-category stabilizes for k >= n+2. We give evidence for this hypothesis and describe its relation to stable homotopy theory. We then propose a description of n-dimensional unitary extended TQFTs as weak n-functors from the "free stable weak n-category with duals on one object" to the n-category of "n-Hilbert spaces". We conclude by describing n-categorical generalizations of deformation quantization and the quantum double construction.},
Author = {Baez, J. and Dolan, J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {q-alg/9503002},
Journal = {J.Math.Phys},
Keywords = {quantum theory; category theory; topology},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/John C. Baez/Higher-dimensional Algebra and Topological Quantum Field.pdf},
Pages = {6073-6105},
Title = {Higher-dimensional Algebra and Topological Quantum Field Theory},
Volume = {36},
Year = {1995},
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@article{Church1940A-Formulation-o,
Author = {Church, A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Journal of Symbolic Logic},
Keywords = {logic; lambda calculus; types},
Title = {A Formulation of the Simple Theory of Types},
Volume = {5},
Year = {1940}}
@article{Svetlichny2006Teleporting-a-q,
Abstract = {If both Alice and Bob have access to a two-qubit "background state" then, by simulating Everett's many worlds interpretation of measurement, Alice can teleport a qubit to Bob, each using fixed unitaries. If Bob has access to only one of the background qubits, teleportation is still possible by Alice sending Bob one classical bit of information gained from a measurement of the other qubit. The Everett picture unifies unitaries, measurements, and classical communication into just unitaries, provided there are background states shared by all parties.},
Author = {Svetlichny, G.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {quant-ph/0610081},
Keywords = {quantum theory;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Svetlichny/Teleporting a qubit a la Everett.pdf},
Title = {Teleporting a qubit a la Everett},
Year = {2006},
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@inproceedings{Selinger2006Idempotents-in-,
Author = {Selinger, P.},
Booktitle = {Proceedings of the 4th International Workshop on Quantum Programming Languages},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Selinger, P.},
Keywords = {category theory; categorical quantum mechanics},
Title = {Idempotents in dagger categories},
Year = {2006}}
@article{Lamarche2006From-Proof-Nets,
Abstract = {In the first part of this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the well-known theory of unit-free multiplicative proof nets. A linking is no longer a set of axiom links but a tree in which the axiom links are subtrees. These trees will be identified according to an equivalence relation based on a simple form of graph rewriting. We show the standard results of sequentialization and strong normalization of cut elimination. In the second part of the paper we show that the identifications enforced on proofs are such that the class of two-conclusion proof nets defines the free *-autonomous category.},
Author = {Lamarche, F. and Strassburger, L.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arxiv:cs.LO/0605054},
Journal = {LMCS},
Keywords = {linear logic; proof-nets; category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Lamarche/From Proof Nets to the Free *-Autonomous.pdf},
Number = {4},
Pages = {3},
Title = {From Proof Nets to the Free *-Autonomous Category},
Volume = {2},
Year = {2006},
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Bdsk-Url-1 = {http://dx.doi.org/10.2168/LMCS-2(4:3)2006}}
@article{Kelly1971Coherence-in-cl,
Author = {Kelly, G.M. and Mac Lane, S.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Journal of Pure and Applied Algebra},
Keywords = {category theory; coherence},
Pages = {97-140},
Title = {Coherence in closed categories},
Volume = {1},
Year = {1971}}
@incollection{Kelly1972Many-variable-f,
Author = {Kelly, G.M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory; coherence},
Pages = {66-105},
Publisher = {Springer},
Series = {Lecture Notes in Mathematics},
Title = {Many-variable functorial calculus {I}},
Volume = {281},
Year = {1972}}
@article{Eilenberg1966A-generalisatio,
Author = {Eilenberg, S. and Kelly, G.M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Journal of Algebra},
Keywords = {category theory; coherence},
Pages = {366-375},
Title = {A generalisation of the functorial calculus},
Volume = {3},
Year = {1966}}
@incollection{Kelly1974On-Clubs-and-Do,
Author = {Kelly, G.M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory; coherence},
Pages = {181-256},
Publisher = {Springer},
Series = {Lecture Notes in Mathematics},
Title = {On Clubs and Doctrines},
Volume = {420},
Year = {1974},
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@incollection{Kelly1972An-Abstract-App,
Author = {Kelly, G.M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory; coherence},
Pages = {106-147},
Publisher = {Springer},
Series = {Lecture Notes in Mathematics},
Title = {An Abstract Approach to Coherence},
Volume = {281},
Year = {1972}}
@article{Mac-Lane1963Natural-Associa,
Author = {Mac Lane, S.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Rice Univ. Studies},
Keywords = {category theory; monoidal categories},
Pages = {28-46},
Title = {Natural Associativity and Commutativity},
Volume = {49},
Year = {1963}}
@article{Jamiolkowski1972,
Author = {Jamio\lkowski, A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Rep. Math. Phys},
Keywords = {quantum theory},
Number = {275},
Title = {An effective method of investigation of positive maps on the set of positive definite operators},
Volume = {3},
Year = {1972}}
@article{Danos2006Determinism-in-,
Abstract = {We introduce a flow condition on open graph states (graph states with inputs and outputs) which guarantees globally deterministic behavior of a class of measurement patterns defined over them. Dependent Pauli corrections are derived for all such patterns, which equalize all computation branches, and only depend on the underlying entanglement graph and its choice of inputs and outputs. The class of patterns having flow is stable under composition and tensorization, and has unitary embeddings as realizations. The restricted class of patterns having both flow and reverse flow supports an operation of adjunction, and has all and only unitaries as realizations.},
Author = {Danos, V. and Kashefi, E.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1103/PhysRevA.74.052310},
Journal = {Phys. Rev. A},
Keywords = {quantum computing; entanglement; ; measurement-based quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Danos/Determinism in the one-way model.pdf},
Number = {052310},
Title = {Determinism in the one-way model},
Volume = {74},
Year = {2006},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.74.052310}}
@article{Conway2006The-Free-Will-T,
Abstract = {On the basis of three physical axioms, we prove that if the choice of a particular type of spin 1 experiment is not a function of the information accessible to the experimenters, then its outcome is equally not a function of the information accessible to the particles. We show that this result is robust, and deduce that neither hidden variable theories nor mechanisms of the GRW type for wave function collapse can be made relativistic. We also establish the consistency of our axioms and discuss the philosophical implications.},
Author = {Conway, J. and Kochen, S.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {quant-ph/0604079 quant-ph/0604079 arxiv:quant-ph/0604079},
Keywords = {quantum computing; quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Conway/The Free Will Theorem.pdf},
Month = {April},
Title = {The Free Will Theorem},
Year = {2006},
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@inproceedings{Coecke2006POVMs-and-Naima,
Author = {Coecke, B. and Paquette, E. O.},
Booktitle = {Proceedings of the 4th International Workshop on Quantum Programming Languages},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0608072},
Keywords = {quantum computing; category theory; compact closed categories},
Pages = {131-152},
Series = {Electronic Notes in Theoretical Computer Science},
Title = {{POVM}s and {N}aimark's Theorem without Sums},
Volume = {210},
Year = {2006},
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@article{Panangaden2004Using-BV-to-Cau,
Author = {Panangaden, P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing; entanglement; proof theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Panangaden/Using BV to Causal Quantum Evolution.pdf},
Title = {Using BV to Causal Quantum Evolution},
Year = {2004},
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@article{Blute2003Discrete-Quantu,
Author = {Blute, R. F. and Ivanov, I. T. and Panangaden, P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Int. J. Theor. Phys.},
Keywords = {quantum theory; linear logic; polycategories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Blute/Discrete Quantum Causal Dynamics.pdf},
Pages = {2025-2041},
Title = {Discrete Quantum Causal Dynamics},
Volume = {42},
Year = {2003},
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@inproceedings{Sabry2003Modelling-quant,
Author = {Sabry, A.},
Booktitle = {Proceedings of the ACM SIGPLAN Workshop on Haskell},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing; programming language},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Sabry/Modelling quantum computing in Haskell.pdf},
Organization = {ACM},
Title = {Modelling quantum computing in Haskell},
Year = {2003},
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Bdsk-Url-1 = {http://portal.acm.org/citation.cfm?id=871900&dl=ACM&coll=&CFID=15151515&CFTOKEN=6184618},
Bdsk-Url-2 = {http://dx.doi.org/10.1145/871895.871900}}
@article{Church1932A-set-of-postul,
Author = {Church, A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Annals of Mathematics},
Keywords = {lambda calculus},
Number = {2},
Pages = {346-3666},
Title = {A set of postulates for the foundation of logic},
Volume = {33},
Year = {1932}}
@book{Barendregt1984The-Lambda-Calc,
Author = {Barendregt, H.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {lambda calculus},
Publisher = {North-Holland Publishing},
Title = {The Lambda Calculus: Its Syntax and Semantics},
Year = {1984}}
@article{Girard1998On-the-meaning-,
Author = {Girard, J.-Y.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic; proof theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Girard/On the meaning of logical rules II multiplicatives and additives.pdf},
Title = {On the meaning of logical rules II : multiplicatives and additives},
Year = {1998},
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@article{GirardGeometry-of-Int3,
Author = {Girard, J.-Y.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic; proof theory; proof-nets},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Girard/Geometry of Interaction III Accomodating the additives.pdf},
Title = {Geometry of Interaction III : Accomodating the additives},
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@article{Girard1999Coherent-Banach,
Author = {Girard, J.-Y.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Girard/Coherent Banach Spaces A Continuous Denotational.pdf},
Title = {Coherent Banach Spaces : A Continuous Denotational Semantics},
Year = {1999},
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@article{Girard2004Between-Logic-a,
Author = {Girard, J.-Y.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Girard/Between Logic and Quantic a tract.pdf},
Title = {Between Logic and Quantic : a tract},
Year = {2004},
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@article{Lambek1968Deductive-Syste,
Author = {Lambek, J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Mathematical Systems Theory},
Keywords = {polycategories; category theory},
Number = {4},
Pages = {287-318},
Title = {Deductive Systems and Categories {I}. Syntactic Calculus and Residuated Categories},
Volume = {2},
Year = {1968},
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@inproceedings{J.-Maraist1995Call-by-name-ca,
Author = {Maraist, J. and Odersky, M. and Turner, D. and Wadler, P.},
Booktitle = {11th International Conference on the Mathematical Foundations of Programming Semantics},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic; programming language; lambda calculus},
Title = {Call-by-name, call-by-value, call-by-need, and the linear lambda calculus},
Year = {1995}}
@inproceedings{OHearn1991Linear-logic-an,
Author = {O'Hearn, P. W.},
Booktitle = {Proceedings of the Conference on Category Theory and Computer Science},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Abramsky, S. and Curien, P. L. and Pitts, A. M. and Pitt, D. H. and Poign{\'e}, A. and Rydeheard, D. E.},
Keywords = {linear logic; programming language},
Pages = {74-93},
Publisher = {Springer-Verlag},
Series = {Lecture Notes in Computer Science},
Title = {Linear logic and interference control: Preliminary report},
Volume = {530},
Year = {1991}}
@inproceedings{Hoffman1999Linear-types-an,
Author = {Hoffman, M.},
Booktitle = {Proceedings of the 14th Symposium on Logic in Computer Science},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic; programming language; complexity},
Organization = {IEEE},
Title = {Linear types and non-size increasing polynomial time computation},
Year = {1999}}
@misc{Fuchs2002Quantum-Mechani,
Abstract = {In this paper, I try to cause some good-natured trouble. The issue is, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion is expressed that no end will be in sight until a means is found to reduce quantum theory to two or three statements of crisp physical (rather than abstract, axiomatic) significance. In this regard, no tool appears better calibrated for a direct assault than quantum information theory. Far from a strained application of the latest fad to a time-honored problem, this method holds promise precisely because a large part---but not all---of the structure of quantum theory has always concerned information. It is just that the physics community needs reminding.},
Author = {Fuchs, C.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {quant-ph/0205039},
Keywords = {quantum theory; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Fuchs/Quantum Mechanics as Quantum Information (and.pdf},
Title = {Quantum Mechanics as Quantum Information (and only a little more)},
Year = {2002},
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@article{Isham2000Some-possible-r,
Author = {Isham, C. J. and Butterfield, J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Foundations of Physics},
Keywords = {toposes; quantum theory},
Pages = {1707 - 1735},
Title = {Some possible roles for topos theory in quantum theory and quantum gravity},
Volume = {30},
Year = {2000}}
@book{Milner1997Definition-of-S,
Author = {Milner, R and Tofte, M. and Harper, R and MacQueen, D.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {programming language},
Publisher = {MIT Press},
Title = {Definition of Standard ML (Revised).},
Year = {1997}}
@electronic{S.L.-Peyton-Jones1999The-Haskell-98-,
Author = {Peyton Jones, S. L. and Hughes, J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {programming language},
Title = {The {H}askell 98 {R}eport},
Year = {1999},
Bdsk-Url-1 = {www.haskell.org}}
@book{Lambek1986Introduction-to,
Author = {Lambek, J. and Scott, P. J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {lambda calculus; category theory; proof theory},
Publisher = {Cambridge University Press},
Series = {Cambridge studies in advanced mathematics},
Title = {Introduction to higher order categorical logic},
Volume = {7},
Year = {1986}}
@book{Prawitz1965Natural-Deducti,
Author = {Prawitz, D.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {proof theory},
Publisher = {Almqvist \& Wiksell},
Title = {Natural Deduction. A Proof-Theoretic Study},
Year = {1965}}
@book{Sorensen2006LECTURES-ON-THE,
Author = {S{\o}rensen, M. H. and Urzyczyn, P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {programming language; lambda calculus; proof theory},
Publisher = {Elsevier},
Series = {Studies in Logic and the Foundations of Mathematics},
Title = {Lectures on the Curry-Howard Isomorphism},
Volume = {149},
Year = {2006}}
@phdthesis{Smets2001The-Logic-of-Ph,
Author = {Smets, S.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum theory; proof theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Smets/The Logic of Physical Properties in Static and Dynamic.pdf},
Month = {May},
School = {Vrije Universiteit Brussel},
Title = {The Logic of Physical Properties in Static and Dynamic Perspective},
Year = {2001},
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Bdsk-Url-1 = {http://www.vub.ac.be/CLEA/sonja/Ph.D.-SONJA.ps}}
@article{Marcelo-Fiore2002Objects-of-Cate,
Abstract = {In many everyday categories (sets, spaces, modules, ...) objects can be both added and multiplied. The arithmetic of such objects is a challenge because there is usually no subtraction. We prove a family of cases of the following principle: if an arithmetic statement about the objects can be proved by pretending that they are complex numbers, then there also exists an honest proof.},
Author = {Fiore, M and Leinster, T.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {math.CT/0212377},
Keywords = {category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Fiore/Objects of Categories as Complex Numbers.pdf},
Month = {December},
Title = {Objects of Categories as Complex Numbers},
Year = {2002},
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@article{Koenraad-M.R.-Audenaert2005Entanglement-on,
Author = {Audenaert, K.M.R. and Plenio, M. B.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {quant-ph/0505036},
Journal = {New J. Phys},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Koenraad M.R. Audenaert/Entanglement on mixed stabiliser states--I Normal.pdf},
Title = {Entanglement on mixed stabiliser states--I: Normal Forms and Reduction Procedures},
Volume = {7},
Year = {2005},
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@article{Baez1997Spin-Foam-Model,
Abstract = {While the use of spin networks has greatly improved our understanding of the kinematical aspects of quantum gravity, the dynamical aspects remain obscure. To address this problem, we define the concept of a `spin foam' going from one spin network to another. Just as a spin network is a graph with edges labeled by representations and vertices labeled by intertwining operators, a spin foam is a 2-dimensional complex with faces labeled by representations and edges labeled by intertwining operators. Spin foams arise naturally as higher-dimensional analogs of Feynman diagrams in quantum gravity and other gauge theories in the continuum, as well as in lattice gauge theory. When formulated as a `spin foam model', such a theory consists of a rule for computing amplitudes from spin foam vertices, faces, and edges. The product of these amplitudes gives the amplitude for the spin foam, and the transition amplitude between spin networks is given as a sum over spin foams. After reviewing how spin networks describe `quantum 3-geometries', we describe how spin foams describe `quantum 4-geometries'. We conclude by presenting a spin foam model of 4-dimensional Euclidean quantum gravity, closely related to the state sum model of Barrett and Crane, but not assuming the presence of an underlying spacetime manifold.},
Author = {Baez, J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {gr-qc/9709052},
Journal = {Class. Quantum Grav},
Keywords = {quantum gravity},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Baez/Spin Foam Models.pdf},
Pages = {1827-1858},
Title = {Spin Foam Models},
Volume = {15},
Year = {1998},
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@book{Kassel1994Quantum-Groups,
Author = {Kassel, C.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum theory; algebra},
Publisher = {Springer},
Title = {Quantum Groups},
Year = {1994}}
@article{Yetter1990Quantales-and-N,
Author = {Yetter, D. N.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Journal of Symbolic Logic},
Keywords = {linear logic},
Number = {1},
Pages = {41-64},
Title = {Quantales and (Noncommutative) Linear Logic},
Volume = {55},
Year = {1990}}
@inproceedings{Nagarajan2006-An-Automated-A,
Author = {Nagarajan, R. and Papanikolaou, N. and Bowen, G. and Gay, S.},
Booktitle = {Proceedings of DCM 2006},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Nagarajan/An Automated Analysis of the Security of Quantum Key Distribution.pdf},
Month = {July},
Title = {An Automated Analysis of the Security of Quantum Key Distribution},
Year = {2006},
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@article{P.-Mateus2005Weakly-complete,
Abstract = {A weakly complete finitary axiomatization for EQPL (exogenous quantum propositional logic) is presented. The proof is carried out using a non trivial extension of the Fagin-Halpern-Megiddo technique together with three Henkin style completions.},
Author = {Mateus, P. and Sernadas, A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {math.LO/0503453},
Keywords = {quantum computing; proof theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Mateus/Weakly complete axiomatization of exogenous quantum.pdf},
Month = {March},
Title = {Weakly complete axiomatization of exogenous quantum propositional logic},
Year = {2005},
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@article{DHondt2006Quantum-Weakest,
Abstract = {We develop a notion of predicate transformer and, in particular, the weakest precondition, appropriate for quantum computation. We show that there is a Stone-type duality between the usual state-transformer semantics and the weakest precondition semantics. Rather than trying to reduce quantum computation to probabilistic programming we develop a notion that is directly taken from concepts used in quantum computation. The proof that weakest preconditions exist for completely positive maps follows immediately from the Kraus representation theorem. As an example we give the semantics of Selinger's language in terms of our weakest preconditions. We also cover some specific situations and exhibit an interesting link with stabilizers. },
Author = {D'Hondt, E. and Panangaden, P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {http://arxiv.org/abs/quant-ph/0501157},
Journal = {Mathematical Structures in Computer},
Keywords = {quantum computing; programming language},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/D'Hondt/Quantum Weakest Preconditions.pdf},
Month = {July},
Number = {3},
Pages = {429-451},
Title = {Quantum Weakest Preconditions},
Volume = {16},
Year = {2006},
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@inproceedings{Alexandru-Baltag2004The-logic-of-qu,
Author = {Baltag, A and Smets, S.},
Booktitle = {Proceedings of the 2nd International Workshop on Quantum Programming Languages},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Selinger, Peter},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Baltag/The logic of quantum programs.pdf},
Month = {July},
Number = {33},
Publisher = {Turku Centre for Computer Science},
Series = {TUCS General Publication},
Title = {The logic of quantum programs},
Year = {2004},
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@article{Maslov2005Toffoli-network,
Abstract = {Reversible logic functions can be realized as networks of Toffoli gates. The synthesis of Toffoli networks can be divided into two steps. First, find a network that realizes the desired function. Second, transform the network such that it uses fewer gates, while realizing the same function. This paper addresses the above synthesis approach. We present a basic method and, based on that, a bidirectional synthesis algorithm which produces a network of Toffoli gates realizing a given reversible specification. An asymptotically optimal modification of the basic synthesis algorithm employing generalized mEXOR gates is also presented. Transformations are then applied using template matching. The basis for a template is a network of gates that realizes the identity function. If a sequence of gates in the synthesized network matches a sequence comprised of more than half the gates in a template, then a transformation using the remaining gates in the template can be applied resulting in a reduction in the gate count for the synthesized network. All templates with up to six gates are described in this paper. Experimental results including an exhaustive examination of all 3-variable reversible functions and a collection of benchmark problems are presented. The paper concludes with suggestions for further research.},
Author = {Maslov, D. and Dueck, G.W. and Miller, D.M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Maslov/Toffoli network synthesis with templates.pdf},
Month = {June},
Number = {6},
Pages = {807-817},
Title = {Toffoli network synthesis with templates},
Volume = {24},
Year = {2005},
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Bdsk-Url-1 = {http://dx.doi.org/10.1109/TCAD.2005.847911}}
@inproceedings{Maslov2005Quantum-Circuit,
Abstract = {Optimal synthesis of quantum circuits is intractable and heuristic methods must be employed. Templates are a general approach to reversible and quantum circuit simplification. In this paper, we consider the use of templates to simplify a quantum circuit initially found by other means. We present and analyze templates in the general case, and then provide particular details for circuits composed of NOT, CNOT and controlled-sqrt-of-NOT gates. We introduce templates for this set of gates and apply them to simplify both known quantum realizations of Toffoli gates and circuits found by earlier heuristic Fredkin and Toffoli gate synthesis algorithms. While the number of templates is quite small, the reduction in quantum cost is often significant.},
Author = {Maslov, D. and Young, C. and Miller, M. and Dueck, D.},
Booktitle = {Proceedings of the conference on Design, Automation and Test in Europe},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Maslov/Quantum Circuit Simplification Using Templates.pdf},
Pages = {1208-1213},
Title = {Quantum Circuit Simplification Using Templates},
Volume = {2},
Year = {2005},
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Bdsk-Url-1 = {http://portal.acm.org/citation.cfm?id=1048925.1049300&coll=&dl=ACM&type=series&idx=1048925&part=Proceedings&WantType=Proceedings&title=Design,%20Automation,%20and%20Test%20in%20Europe&CFID=15151515&CFTOKEN=6184618},
Bdsk-Url-2 = {http://dx.doi.org/10.1109/DATE.2005.249}}
@article{Metayer2001Implicit-exchan,
Author = {M{\'e}tayer, F.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Mathematical Structures in Computer Science},
Keywords = {linear logic; proof-nets; topology},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Métayer/Implicit exchange in multiplicative proofnets.pdf},
Number = {2},
Pages = {261-272},
Title = {Implicit exchange in multiplicative proofnets},
Volume = {11},
Year = {2001},
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Bdsk-Url-1 = {http://www.pps.jussieu.fr/~metayer/PDF/implex.pdf.gz}}
@misc{Jozsa2006On-the-Simulati,
Author = {Jozsa, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {quant-ph/0603163},
Keywords = {quantum computing; complexity},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Jozsa/On the Simulation of Quantum Circuits.pdf},
Title = {On the Simulation of Quantum Circuits},
Year = {2006},
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@article{Deutsch1992Rapid-Solution-,
Author = {Deutsch, D. and Jozsa, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Proceedings of the Royal Society of London A},
Keywords = {quantum computing},
Pages = {553},
Title = {Rapid Solution of Problems by Quantum Computation},
Volume = {454},
Year = {1992}}
@article{Deutsch1985Quantum-Theory-,
Author = {Deutsch, D.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Proceedings of the Royal Society of London A},
Keywords = {quantum computing},
Pages = {97},
Title = {Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer},
Volume = {400},
Year = {1985}}
@article{Manin1980Computable-and-,
Author = {Manin, Y.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Sovetskoye Radio},
Keywords = {quantum computing},
Note = {In {R}ussian.},
Title = {Computable and Uncomputable},
Year = {1980}}
@article{Sassone2002Deriving-Bisimu,
Author = {Sassone, V. and Sobocinski, P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Electronic Notes in Theoretical Computer Science},
Keywords = {bigraphs; process algebra; category theory},
Number = {2},
Title = {Deriving Bisimulation Congruences: a 2-categorical approach},
Volume = {68},
Year = {2002}}
@inproceedings{Milner2001Bigraphical-Rea,
Author = {Milner, R.},
Booktitle = {Proceedings of the 12th International Conference on Concurrency Theory},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {process algebra; bigraphs},
Pages = {16-35},
Series = {Lecture Notes in Computer Science},
Title = {Bigraphical Reactive Systems},
Volume = {2154},
Year = {2001}}
@inproceedings{Vincent-Danos2005Distributed-mea,
Abstract = {We develop a formal model for distributed measurement-based quantum computations, adopting an agent-based view, such that computations are described locally where possible. Because the network quantum state is in general entangled, we need to model it as a global structure, reminiscent of global memory in classical agent systems. Local quantum computations are described as measurement patterns. Since measurement-based quantum computation is inherently distributed, this allows us to extend naturally several concepts of the measurement calculus, a formal model for such computations. Our goal is to define an assembly language, i.e. we assume that computations are well-defined and we do not concern ourselves with verification techniques. The operational semantics for systems of agents is given by a probabilistic transition system, and we define operational equivalence in a way that it corresponds to the notion of bisimilarity. With this in place, we prove that teleportation is bisimilar to a direct quantum channel, and this also within the context of larger networks.},
Author = {Danos, V and D'Hondt, E. and Kashefi, E. and Panangaden, P.},
Booktitle = {Proceedings of the 3rd International Workshop on Quantum Programming Languages},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {quant-ph/0506070},
Keywords = {quantum computing; ; measurement-based quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Vincent Danos/Distributed measurement-based quantum computation.pdf},
Month = {June},
Title = {Distributed measurement-based quantum computation},
Year = {2005},
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@article{Danos2004Robust-and-pars,
Author = {Danos, Vincent and Kashefi, Elham and Panangaden, Prakash},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {quant-ph/0411071},
Journal = {Phys. Rev. A},
Keywords = {quantum computing; ; measurement-based quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Danos/Robust and parsimonious realisations of unitaries in the one-way.pdf},
Month = {December},
Number = {6},
Pages = {060101},
Title = {Robust and parsimonious realisations of unitaries in the one-way model},
Volume = {72},
Year = {2004},
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Bdsk-Url-1 = {http://link.aps.org/abstract/PRA/v72/e064301},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevA.72.064301}}
@article{Jozsa2004Illustrating-th,
Abstract = {Over the past decade, quantum information theory has developed into a vigorous field of research despite the fact that quantum information, as a precise concept, is undefined. Indeed, the very idea of viewing quantum states as carriers of some kind of information (albeit unknowable in classical terms) leads naturally to interesting questions that might otherwise never have been asked, and corresponding new insights. We discuss some illustrative examples, including a strengthening of the well-known no-cloning theorem leading to a property of permanence for quantum information, and considerations arising from information compression that reflect on fundamental issues.},
Author = {Jozsa, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {IBM Journal of Research and Development},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Jozsa/Illustrating the concept oof quantum information.pdf},
Month = {January},
Number = {1},
Title = {Illustrating the concept of quantum information},
Volume = {48},
Year = {2004},
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Bdsk-Url-1 = {http://www.research.ibm.com/journal/rd/481/jozsa.html},
Bdsk-Url-2 = {http://dx.doi.org/10.1147/rd.481.0079}}
@article{Pati2000Impossibility-o,
Abstract = {A photon in an arbitrary polarization state cannot be cloned perfectly. But suppose that at our disposal we have several copies of a photon in an unknown state. Is it possible to delete the information content of one or more of these photons by a physical process? Specifically, if two photons are in the same initial polarization state, is there a mechanism that produces one photon in the same initial state and the other in some standard polarization state? If this could be done, then one would create a standard blank state onto which one could copy an unknown state approximately, by deterministic cloning or exactly, by probabilistic cloning. This could in principle be useful in quantum computation, where one could store some information in an already computed state by deleting the old information. Here we show that the linearity of quantum theory does not allow us to delete a copy of an arbitrary quantum state perfectly. Though in a classical computer information can be deleted (reversibly) against a copy, the analogous task cannot be accomplished, even irreversibly, with quantum information.},
Author = {Pati, A.K. and Braunstein, S. L.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Nature},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Pati/Impossibility of deleting an unknown quantum state.pdf},
Pages = {164-165},
Title = {Impossibility of deleting an unknown quantum state},
Volume = {404},
Year = {2000},
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Bdsk-Url-1 = {http://www-users.cs.york.ac.uk/schmuel/papers/pb00.pdf}}
@book{Dosen2005Proof-Net-Categ,
Author = {Do\v{s}en, K. and Petri\'{c}, Z.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {proof-nets; linear logic; monoidal categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Dosen/Proof-Net Categories.pdf},
Publisher = {Mathematical Institute, Belgrade},
Title = {Proof-Net Categories},
Year = {2005},
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@book{Curry1958Combinatory-Log,
Author = {Curry, H. B. and Feys, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {lambda calculus},
Publisher = {North-Holland Publishing},
Title = {Combinatory Logic I},
Year = {1958}}
@book{Barwise-1977-Handbook,
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Barwise, J.},
Keywords = {logic;},
Publisher = {North-Holland Publishing},
Title = {The Handbook of Mathematical Logic},
Year = {1977}}
@incollection{Gentzen1935Untersuchungen,
Author = {Gentzen, G.},
Booktitle = {The Collected Papers of Gerhard Gentzen},
Crossref = {1969Collected-Gentzen},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Title = {Untersuchungen {\"u}ber das Schliessen},
Year = {1935}}
@incollection{Lambek-2005-bicats,
Author = {Lambek, J.},
Booktitle = {Linear Logic in Computer Science},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Ruet, P.},
Keywords = {polycategories; category theory},
Title = {Bicategories in algebra and linguistics},
Year = {2005}}
@book{1969Collected-Gentzen,
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Szabo, M.E},
Keywords = {proof theory; logic},
Publisher = {North-Holland Publishing},
Title = {The Collected Papers of Gerhard Gentzen},
Year = {1969}}
@book{Dummett1977Elements-of-Int,
Author = {Dummett, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {logic; proof theory; foundations of mathematics},
Publisher = {Oxford University Press},
Series = {Oxford Logic Guides},
Title = {Elements of Intuitionism},
Year = {1977}}
@incollection{Buss1998Handbook-of-Pro,
Author = {Buss, S.},
Booktitle = {Handbook of Proof Theory},
Crossref = {1998Handbook-ProofTheory},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Title = {First Order Proof Theory of Arithmetic}}
@incollection{Buss1998Introduction-to,
Author = {Buss, S.},
Booktitle = {Handbook of Proof Theory},
Crossref = {1998Handbook-ProofTheory},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Title = {Introduction to Proof Theory}}
@book{1998Handbook-ProofTheory,
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Buss, S.},
Keywords = {proof theory; logic},
Publisher = {Elsevier Science Publishers B.V.},
Title = {Handbook of Proof Theory},
Year = {1998}}
@article{Boolos1984Dont-Eliminate-,
Author = {Boolos, J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Journal of Philosophical Logic},
Keywords = {proof theory;},
Pages = {373-378},
Title = {Don't Eliminate Cut},
Volume = {13},
Year = {1984}}
@book{Beth1959Foundations-of-,
Author = {Beth, E.W.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {logic; proof theory; recursion theory; foundations of mathematics},
Publisher = {North-Holland Publishing},
Title = {Foundations of Mathematics},
Year = {1959}}
@book{1990Handbook-TCS-b,
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {van Leeuwen, J.},
Keywords = {logic},
Publisher = {Elsevier Science Publishers B.V.},
Title = {The Handbook of Theoretical Computer Science},
Volume = {B},
Year = {1990}}
@incollection{Apt1990Logic-Programmi,
Author = {Apt, K.R.},
Booktitle = {The Handbook of Theoretical Computer Science},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {van Leeuwen, J.},
Keywords = {logic; programming language; proof theory; surveys},
Publisher = {Elsevier Science Publishers B.V.},
Title = {Logic Programming},
Volume = {B},
Year = {1990}}
@book{Hindley1986Introduction-to,
Author = {Hindley, R.J. and Seldin, J. P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {lambda calculus; types; combinatory logic; programming language},
Publisher = {Cambridge University Press},
Series = {London Mathematical Society Student Texts},
Title = {Introduction to Combinators and $\lambda$-Calculus},
Volume = {1},
Year = {1986}}
@book{Hindley1997Basic-Simple-Ty,
Author = {Hindley, R.J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {programming language; proof theory; lambda calculus, types},
Publisher = {Cambridge University Press},
Series = {Cambridge Tracts in Theoretical Computer Science},
Title = {Basic Simple Type Theory},
Volume = {42},
Year = {1997}}
@book{Peres1993Quantum-Theory,
Author = {Peres, A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum theory; physics},
Publisher = {Kluwer Academic},
Title = {Quantum Theory: Concepts and Methods},
Year = {1993}}
@inproceedings{LaurentSlicing-Polariz,
Author = {Laurent, O. and Tortora de Falco, L.},
Booktitle = {Linear Logic in Computer Science},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Ehrhard, T. and Girard, J.-Y. and Ruet, P. and Scott, P.},
Keywords = {linear logic; proof-nets ; proof theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Laurent/Slicing Polarized Additive Normalisation.pdf},
Pages = {247--282},
Publisher = {Cambridge University Press},
Series = {London Mathematical Society Lecture Notes},
Title = {Slicing Polarized Additive Normalisation},
Volume = {316},
Year = {2004},
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@book{Kelly1982Basic-Concepts-,
Author = {Kelly, G.M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {enriched categories, monoidal categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Kelly/Basic Concepts of Enriched Category Theory.pdf},
Number = {64},
Publisher = {Cambridge University Press},
Series = {Lecture Notes in Mathematics},
Title = {Basic Concepts of Enriched Category Theory},
Year = {1982},
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Bdsk-Url-1 = {http://www.tac.mta.ca/tac/reprints/articles/10/tr10abs.html}}
@article{Kauffman2006q---Deformed-Sp,
Annote = {We review the q-deformed spin network approach to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. Our methods are rooted in the bracket state sum model for the Jones polynomial. We give our results for a large class of representations based on values for the bracket polynomial that are roots of unity. We make a separate and self-contained study of the quantum universal Fibonacci model in this framework. We apply our results to give quantum algorithms for the computation of the colored Jones polynomials for knots and links, and the Witten-Reshetikhin-Turaev invariant of three manifolds.},
Author = {Kauffman, L. H. and Lomonaco Jr, S. J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arxiv:quant-ph/0606114},
Keywords = {quantum computing, category theory, topology, quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Kauffman/$q$ - Deformed Spin Networks, Knot Polynomials.pdf},
Month = {June},
Title = {$q$ - Deformed Spin Networks, Knot Polynomials and Anyonic Topological Quantum Computation},
Year = {2006},
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@article{Aaronson2004Quantum-Computi,
Abstract = {I study the class of problems efficiently solvable by a quantum computer, given the ability to "postselect" on the outcomes of measurements. I prove that this class coincides with a classical complexity class called PP, or Probabilistic Polynomial-Time. Using this result, I show that several simple changes to the axioms of quantum mechanics would let us solve PP-complete problems efficiently. The result also implies, as an easy corollary, a celebrated theorem of Beigel, Reingold, and Spielman that PP is closed under intersection, as well as a generalization of that theorem due to Fortnow and Reingold. This illustrates that quantum computing can yield new and simpler proofs of major results about classical computation.},
Author = {Aaronson, S.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {quant-ph/0412187},
Journal = {Proceedings of the Royal Society A},
Keywords = {quantum computing, complexity},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Aaronson/Quantum Computing, Postselection, and Probabilistic Polynomial-Time.pdf},
Number = {2063},
Pages = {3473-3482},
Title = {Quantum Computing, Postselection, and Probabilistic Polynomial-Time},
Volume = {461},
Year = {2005},
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@article{Ying2006Quantum-loop-pr,
Abstract = {Loop is a powerful program construct in classical computation, but its power is still not exploited fully in quantum computation. The exploitation of such power definitely requires a deep understanding of the mechanism of quantum loop programs. In this paper, we introduce a general scheme of quantum loops. The computational process of a quantum loop is then described. Moreover, the notions of termination and almost termination are proposed for quantum loops. The function computed by a quantum loop is also defined. To illustrate these notions, we carefully examine two simplest classes of quantum loop programs: one qubit quantum loops, and two qubit quantum loops defined by controlled gates. In particular, we find a necessary and sufficient condition for termination of a general quantum loop on any mixed input state. A necessary and sufficient condition for almost termination on a pure input state is given too.},
Author = {Ying, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arxiv:quant-ph/0605218},
Keywords = {quantum computing; programming language},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Ying/Quantum loop programs.pdf},
Month = {May},
Title = {Quantum loop programs},
Year = {2006},
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@book{Geroch1985Mathematical-Ph,
Address = {Chicago},
Author = {Geroch, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {physics; topology; algebra},
Publisher = {University of Chicago Press},
Series = {Chicago Lectures in Physics},
Title = {Mathematical Physics},
Year = {1985}}
@article{Oliveira2006Efficient-Gener,
Abstract = {We find that generic entanglement is physical, in the sense that it can be generated in polynomial time from two-qubit gates picked at random. We prove as the main result that such a process generates the average entanglement of the uniform (Haar) measure in at most $O(N^3)$ steps for $N$ qubits. This is despite an exponentially growing number of such gates being necessary for generating that measure fully on the state space. Numerics furthermore show a variation cut-off allowing one to associate a specific time with the achievement of the uniform measure entanglement distribution. Various extensions of this work are discussed. The results are relevant to entanglement theory and to protocols that assume generic entanglement can be achieved efficiently.},
Author = {Oliveira, R. and Dahlsten, O.C.O. and Plenio, M.B.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arxiv:quant-ph/0605126},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Oliveira/Efficient Generation of Generic Entanglement.pdf},
Month = {May},
Title = {Efficient Generation of Generic Entanglement},
Year = {2006},
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@article{Terhal2004Is-entanglement,
Abstract = {In this paper I discuss some of the early history of quantum information theory. By considering the question of whether entanglement is ``monogamous,'' I illustrate Charles Bennett's influence on modern quantum information theory. Finally, I review our recent answers to this entanglement question and its relation to Be},
Author = {Terhal, B. M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {IBM Journal of Research and Development},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Terhal/Is entanglement monogamous?.pdf},
Number = {1},
Title = {Is entanglement monogamous?},
Volume = {48},
Year = {2004},
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Bdsk-Url-2 = {http://dx.doi.org/10.1147/rd.481.0071}}
@article{O.A.-Nagel2003Another-state-e,
Abstract = {We propose a measure of state entanglement for states of the tensor-product of C*-algebras.},
Author = {Nagel, O.A. and Raggio, G.A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {quant-ph/0306024},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/O.A. Nagel/Another state entanglement measure.pdf},
Title = {Another state entanglement measure},
Year = {2003},
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@article{Rovelli1998Loop-Quantum-Gr,
Author = {Rovelli, Carlo},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Living Reviews in Relativity},
Keywords = {quantum gravity},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Rovelli/Loop Quantum Gravity.pdf},
Month = {January},
Title = {Loop Quantum Gravity},
Year = {1998},
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@article{Houston2006Finite-Products,
Abstract = {If a compact closed category has finite products or finite coproducts then it in fact has finite biproducts, and so is semi-additive.},
Author = {Houston, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:math.CT/0604542},
Journal = {Journal of Pure and Applied Algebra},
Keywords = {compact closed categories; category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Houston/Finite Products are Biproducts in a Compact Closed.pdf},
Month = {June},
Number = {2},
Pages = {394-400},
Title = {Finite Products are Biproducts in a Compact Closed Category},
Volume = {212},
Year = {2008},
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Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.jpaa.2007.05.021}}
@article{Pawel-KurzynskiGraphical-repre,
Abstract = {We present graphical representation for genaralized quantum measurements (POVM). We represent POVM elements as Bloch vectors and find the conditions these vectors should satisfy in order to describe realizable physical measurements. We show how to find probability of measurement outcome in a graphical way. The whole formalism is applied to unambigous discrimination of nonorthogonal quantum states.},
Author = {Kurzynski, P. and Grudka, A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0604189},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Kurzynski/Graphical representation of generalized quantum measurements.pdf},
Title = {Graphical representation of generalized quantum measurements},
Year = {2006},
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@phdthesis{Christandl2006The-Structure-o,
Abstract = {This thesis presents a study of the structure of bipartite quantum states. In the first part, the representation theory of the unitary and symmetric groups is used to analyse the spectra of quantum states. In particular, it is shown how to derive a one-to-one relation between the spectra of a bipartite quantum state and its reduced states, and the Kronecker coefficients of the symmetric group. In the second part, the focus lies on the entanglement of bipartite quantum states. Drawing on an analogy between entanglement distillation and secret-key agreement in classical cryptography, a new entanglement measure, `squashed entanglement', is introduced.},
Annote = {Part I contains results from quant-ph/0409016 and quant-ph/0511029, and analyses Horn's problem in this context. Part II reviews entanglement measures, presents results from quant-ph/0308088 and quant-ph/0501090, and provides new material on entanglement measures, information-gain versus disturbance tradeoffs and cheat sensitive quantum string commitment},
Author = {Christandl, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arxiv:quant-ph/0604183},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Christandl/The Structure of Bipartite Quantum States - Insights.pdf},
Month = {April},
School = {University of Cambridge},
Title = {The Structure of Bipartite Quantum States - Insights from Group Theory and Cryptography},
Year = {2006},
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@article{Martin-Daumer2006The-Message-of-,
Abstract = {We criticize speculations to the effect that quantum mechanics is fundamentally about information. We do this by pointing out how unfounded such speculations in fact are. Our analysis focuses on the dubious claims of this kind recently made by Anton Zeilinger.},
Author = {Daumer, M. and Duerr, D. and Goldstein, S. and Maudlin, T. and Tumulka, R. and Zanghi, N.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0604173},
Keywords = {quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Daumer/The Message of the Quantum?.pdf},
Title = {The Message of the Quantum?},
Year = {2006},
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@article{Zeilinger2005The-message-of-,
Abstract = {Einstein challenged physics to describe "the real factual situation". But an understanding of the very concepts that he criticized a century ago may provide the best clues yet about reality 'out there'.},
Author = {Zeilinger, A},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Nature},
Keywords = {quantum theory; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Zeilinger/The message of the quantum.pdf},
Month = {December},
Number = {2005},
Pages = {743},
Title = {The message of the quantum},
Volume = {438},
Year = {2005},
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Bdsk-Url-1 = {http://www.nature.com/nature/journal/v438/n7069/full/438743a.html},
Bdsk-Url-2 = {http://dx.doi.org/10.1038/438743a}}
@inbook{Eisert,
Abstract = {We review the theory of multi-particle entanglement. In this book chapter we aim at briefly ``setting the coordinates'' and guiding through the extensive literature in this field. Our coordinate system chosen for this chapter has the axes labeled pure and mixed states on the one hand, entanglement in single specimens and the asymptotic setting on the other hand. We very briefly mention ways to detect multi-particle entanglement, and introduce the concepts of stabilizer and graph states.},
Author = {Eisert, J and Gross, D.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0505149},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Eisert/.pdf},
Title = {Multi-particle entanglement},
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@article{Gay2005Quantun-Program,
Author = {Gay, S.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Bulletein of the EATCS},
Keywords = {quantum computing; programming language},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Gay/Quantun Programming Languages.pdf},
Month = {June},
Title = {Quantun Programming Languages},
Year = {2005},
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Bdsk-Url-1 = {http://www.dcs.gla.ac.uk/~simon/quantum}}
@article{AbrDun:CQLv2:2004,
Abstract = {We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with biproducts on a given category with an involution. This syntax can be used to represent and reason about quantum processes.},
Annote = {This is the journal version -- don't have the number etc yet. Informal version is AbrDun:CQLv2:2004},
Author = {Abramsky, S. and Duncan, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1017/S0960129506005275},
Eprint = {arXiv:quant-ph/0512114},
Journal = {Mathematical Structures in Computer Science},
Keywords = {quantum computing; compact closed categories; proof-nets},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Abramsky/A Categorical Quantum Logic.pdf},
Note = {Special Issue for the Proceedings of QPL 2004},
Number = {3},
Pages = {469-489},
Title = {A Categorical Quantum Logic},
Volume = {16},
Year = {2006},
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Bdsk-Url-1 = {http://dx.doi.org/10.1017/S0960129506005275}}
@unpublished{Brotherston2003A-formal-semant,
Author = {Brotherston, J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {proof theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Brotherston/A formal semantics for the intuitionistic theory of ordinary.pdf},
Month = {March},
Note = {maunscript},
Title = {A formal semantics for the intuitionistic theory of ordinary inductive definitions},
Year = {2003},
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@article{Bellin1994On-the-pi-calcu,
Author = {Bellin, G. and Scott, P. J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Theoretical Computer Science},
Keywords = {linear logic; process algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Bellin/On the $\pi$-calculus and linear logic.pdf},
Title = {On the $\pi$-calculus and linear logic},
Year = {1994},
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@article{Boykin2004Information-vs.,
Author = {Boykin, P. O. and Roychowdhury, V. P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0412028},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Boykin/Information vs. disturbance in dimension D.pdf},
Title = {Information vs. disturbance in dimension {D}},
Year = {2004},
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@article{Bose1998Multiparticle-g,
Abstract = {We generalize the procedure of entanglement swapping to obtain a scheme for manipulating entanglement in multiparticle systems. We describe how this scheme allows one to establish multiparticle entanglement between particles belonging to distant users in a communication network through a prior distribution of singlets followed by only local measurements. We show that this scheme can be regarded as a method of generating entangled states of many particles and compare it with existing schemes using simple quantum computational networks. We highlight the practical advantages of using a series of entanglement swappings during the distribution of entangled particles between two parties. Applications of multiparticle entangled states in cryptographic conferencing and in reading messages from more than one source through a single measurement are also described.},
Author = {Bose, S. and Vedral, V. and Knight, P. L.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev. A},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Bose/Multiparticle generalisation of entanglement swapping.pdf},
Number = {2},
Pages = {822},
Title = {Multiparticle generalisation of entanglement swapping},
Volume = {57},
Year = {1998},
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@article{Bouda2001Entanglement-Sw,
Abstract = {We generalize the entanglement swapping scheme originally proposed for two pairs of qubits to an arbitrary number q of systems composed from an arbitrary number m_j of qudits. Each of the systems is supposed to be prepared in a maximally entangled state of m_j qudits, while different systems are not correlated at all. We show that when a set of \00 $\Sigma^q_{j =1} a_j$ particles (from each of the q systems a_j particles are measured) is subjected to a generalized Bell type measurement, the resulting set of $\Sigma^q_{j =1}(m_j a_j )$ particles will collapse into a maximally entangled state. },
Author = {Bouda, J. and Buzek, V.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Journal of Physics A : mathematical and general},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Bouda/Entanglement Swapping between multi-qudit systems.pdf},
Pages = {4301-4311},
Title = {Entanglement Swapping between multi-qudit systems},
Volume = {34},
Year = {2001},
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@article{Baez2004The-Meaning-of-,
Author = {Baez, J. and Bunn, E. F.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:gr-qc/0103044},
Keywords = {relativity},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Baez/The Meaning of Einstein's equation.pdf},
Month = {August},
Title = {The Meaning of {E}instein's equation},
Year = {2004},
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@misc{Baez2005Loop-Quantum-Gr,
Author = {Baez, J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Howpublished = {Lecture Slides at ACM-SIAM Symposium on Discrete Algorithms},
Keywords = {quantum theory; quantum gravity},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Baez/Loop Quantum Gravity.pdf},
Month = {January},
Title = {Loop Quantum Gravity},
Year = {2005},
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@article{Barr1996The-Chu-Constru,
Author = {Barr, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Theory and Applications of Categories},
Keywords = {category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Barr/The Chu Construction.pdf},
Number = {2},
Pages = {17-35},
Title = {The Chu Construction},
Volume = {2},
Year = {1996},
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@phdthesis{Hines1997The-Algebra-of-,
Address = {Dean Street, Bangor, Gwynedd LL57 1 UT, UK},
Author = {Hines, P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Hines/The Algebra of Self Similarity and its applications.pdf},
Month = {May},
School = {University of Wales, Bangor},
Title = {The Algebra of Self Similarity and its applications},
Year = {1997},
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@article{HinesThe-Unitary-Tra,
Abstract = {In order to describe conditional iteration in quantum systems, we consider structures similar to Unique Decomposition categories (UDCs), where enrichment is taken over a weak version of ?-monoids, giving D. Higgs' \Sigma-groups as a special case. This gives a weaker version of the partition-associativity axiom, removing the requirement that x + y = 0 => x = y = 0 whilst still allowing for a number of constructions based on UDCs, including the standard, or `particle-style', trace. We demonstrate that the category of continuous maps on Hilbert spaces is a weak (in fact, group-like) Unique Decomposition Category (wUDC) with a partially defined standard trace. This trace formula converges for unitary maps, but has no quantum-physical interpretation, since the trace of a unitary is neither unitary nor Hermitian. We then give a construction that splits the trace into the composite of three maps: a canonical inclusion, a unitary operation, and a co-diagonal. We show that this unitary operation is a standard trace in a larger category, and demonstrate how the familiar programming language interpretation of `conditional loops' (via a standard trace over coproducts) gives a semantics of purely quantum while loops conditioned on a quantum variable. Algorithms and physical interpretations are given. },
Author = {Hines, P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Mathematical Structures in Computer Science},
Keywords = {quantum computing; category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Hines/The Unitary Trace on Hilbert spaces, and implementing.pdf},
Note = {manuscript},
Title = {The Unitary Trace on Hilbert spaces, and implementing quantum While loops},
Volume = {submitted},
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@unpublished{Hines2004Unitary-computa,
Abstract = {It is folklore that a quantum computer whose execution is decribed by purely unitary maps is unable to perform variable-length iteration conditioned on a quantum variable, rather than the result of a measurement. As an illustration that this need not be the case, we describe a quantum computation of factorials, using only unitary maps. The resulting computation respects superpositions, so that we may form superpositions of all factorials of integers in a certain range. We may also produce highly entangled resources giving correlations between representations of n and n!, via bipartite measurements. },
Author = {Hines, P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Hines/Unitary computations of factorials.pdf},
Note = {manuscript},
Title = {Unitary computations of factorials},
Year = {2004},
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@unpublished{Hines2004Can-the-von-Neu,
Abstract = {The notion that program code may be stored and manipulated in the same way as data is at the core of the von Neumann architecture, and its implementation as the Fetch-Execute cycle. Classically, the data / code interchangeability is a form of currying, and --- in the language of category theory --- Cartesian closure. In this paper, we consider whether a quantum analog of this exists. A standard result is that quantum program code must be encoded on an orthonormal basis, and this has been interpreted as stating that program code for a quantum computer ''might as well be classical''. We argue that this implies a fully quantum (i.e. based on unitary operations) lambda calculus is not physically realisable, in that it is not possible to `promote an arbitrary quantum register to an operation', and vice versa, in a unitary setting. We also consider the abstract theory of currying in the context of Hilbert space, along with its physical interpretation as teleportation-like protocols. This allows for unrestricted (albeit non-deterministic) promotion of data to code. We also demonstrate that the abstraction operation --- the construction of a quantum resource corresponding to an operation --- is realisable in a single-step operation, unlike the classical case. },
Author = {Hines, P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Hines/Can the von Neumann architecture be made quantum?.pdf},
Note = {manuscript},
Title = {Can the von {Neumann} architecture be made quantum?},
Year = {2004},
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@article{Bartlett20006Degradation-of-,
Abstract = {We investigate the degradation of reference frames, treated as dynamical quantum systems, and quantify their longevity as a resource for performing tasks in quantum information processing. We adopt an operational measure of a reference frame's longevity, namely, the number of measurements that can be made against it with a certain error tolerance. We investigate two distinct types of reference frame: a reference direction, realized by a spin-j system, and a phase reference, realized by an oscillator mode with bounded energy. For both cases, we show that our measure of longevity increases quadratically with the size of the reference system and is therefore non-additive. For instance, the number of measurements that a directional reference frame consisting of N parallel spins can be put to use scales as N^2. Our results quantify the extent to which microscopic or mesoscopic reference frames may be used for repeated, high-precision measurements, without needing to be reset --a question that is important for some implementations of quantum computing. We illustrate our results using the proposed single-spin measurement scheme of magnetic resonance force microscopy. },
Author = {Bartlett, S. D. and Rudolph, T. and Spekkens, R. W. and Turner, P. S.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0602069},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Bartlett/Degradation of a quantum reference frame.pdf},
Title = {Degradation of a quantum reference frame},
Year = {2006},
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@article{Vedral1997Entanglement-Me,
Author = {Vedral, V. and Plenio, M.B.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/9707035},
Journal = {Phys. Rev. A},
Keywords = {entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Vedral/Entanglement Measures and Purification Procedures.pdf},
Pages = {1619-1633},
Title = {Entanglement Measures and Purification Procedures},
Volume = {57},
Year = {1998},
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@article{Horodecki1996Quantum--entrop,
Abstract = {Quantum $\alpha$-entropy inequalities equivalent to Bell's inequality for pure states are considered in the context of the local hidden variable (LHV) model and compared with Bell's inequalities. For $\alpha = 1,2$ they are shown to be satisfied by convex combinations of product states and Werner's mixtures admitting the model. The 2-entropy inequality is proven to be stronger than Bell's inequality in the case. In the latter, the $\alpha$-entropy inequalities taken as a joint condition exclude teleportation admitted in spite of the existence of the LHV model for the Werner-Popescu states. },
Author = {Horodecki, R. and Horodecki, P. and Horodecki, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Lett. A},
Keywords = {entanglement; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Horodecki/Quantum $\alpha$-entropy inequalities independent condition.pdf},
Pages = {377},
Title = {Quantum $\alpha$-entropy inequalities: independent condition for local realism?},
Volume = {210},
Year = {1996},
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Bdsk-Url-1 = {http://dx.doi.org/10.1016/0375-9601(95)00930-2}}
@article{Gisin1991Bells-inequalit,
Abstract = {We prove that any non-product state of two-particle systems violates a Bell inequality.},
Annote = {This is a short (< 2 page) letter, which does exactly what it says in the title: only product states may satisfy Bell's inequality.},
Author = {Gisin, N.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Lett. A},
Keywords = {entanglement; quantum computing},
Month = {April},
Number = {5,6},
Pages = {201-202},
Title = {Bell's inequality holds for all non-product states},
Volume = {154},
Year = {1991},
Bdsk-Url-1 = {http://dx.doi.org/10.1016/0375-9601(91)90805-I}}
@article{Gisin1996Hidden-quantum-,
Abstract = {A family of two spin states with the following properties is presented. These states are "local" in the sense that they do not violate any Bell---CHSH inequality. However, after each spin interacts with two independent local environments, the resulting states of the two spin systems violate a Bell inequality. It is argued that: (1) The problem of classifying the nonlocal states of two spin systems is still open. In particular, for mixed states the violation of Bell's inequality and the concept of nonlocality differ, (2) The fact that some dissipative environments can increase quantum correlations might be useful for quantum computation. (3) Careless application of generalized quantum measurements can violate Bell's inequality by more than 2 \sqrt 2, even for mixtures of product states.},
Author = {Gisin, N.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Lett. A},
Keywords = {entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Gisin/Hidden quantum nonlocality revealed by local.pdf},
Month = {January},
Number = {3},
Pages = {151-156},
Title = {Hidden quantum nonlocality revealed by local filters},
Volume = {210},
Year = {1996},
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@article{Horodecki1996Information-the,
Abstract = {Information-theoretic aspects of quantum inseparability of mixed states are investigated in terms of the $\alpha$-entropy inequalities and teleportation fidelity. Inseparability of mixed states is defined and a complete characterization of the inseparable $2\times2$ systems with maximally disordered subsystems is presented within the Hilbert-Schmidt space formalism. A connection between teleportation and negative conditional $\alpha$-entropy is also emphasized.},
Author = {Horodecki, R. and Horodecki, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/9607007},
Journal = {Phys. Rev. A},
Keywords = {entanglement; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Horodecki/Information-theoretic aspects of quantum inseparability of mixed.pdf},
Pages = {1838},
Title = {Information-theoretic aspects of quantum inseparability of mixed states},
Volume = {54},
Year = {1996},
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@article{Fitzi2001Quantum-Solutio,
Author = {Fitzi, M. and Gisin, N. and Maurer, U.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev. Lett.},
Keywords = {entanglement, algorithms, quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Fitzi/Quantum Solution to the Byzantine Agreement Problem.pdf},
Number = {21},
Title = {Quantum Solution to the Byzantine Agreement Problem},
Volume = {87},
Year = {2001},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.87.217901}}
@inproceedings{Coecke2005De-linearizing-,
Abstract = { Elaborating on our joint work with Abramsky we further unravel the linear structure of Hilbert spaces into several constituents which play different roles in quantum mechanics. Some prove to be very crucial for particular features of the theory while others obstruct the passage to a formalism which is not saturated with physically insignificant global phases. In particular do we pass from a vector space formalism to a rather projective one as it was intended in the (in)famous Birkhoff-von Neumann paper. The bulk of the linear structure required to reason about quantum mechanics is multiplicative since it arises from the strongly compact closed tensor which, besides providing a variety of notions such as scalars, trace, unitarity, self-adjointness and bipartite projectors, Hilbert-Schmidt norm, Hilbert-Schmidt inner-product, and most importantly, the passage from a formalism of the vector space kind to a rather projective one in terms of the preparation-state agreement axiom. Additive types for objects including a zero object provide pseudo-projections from which measurements can be build, and the correctness proofs of the protocols discussed in [Abramsky and Coecke LiCS'04] carry over to the resulting weaker setting. A full probabilistic calculus is obtained when the trace is moreover pseudo-linear and satisfies the diagonal axiom, which brings us to our main result, characterization of the necessary and sufficient additive structure of a both qualitatively and quantitatively effective categorical quantum formalism without redundant global phases.},
Author = {Coecke, B.},
Booktitle = {Proceedings of the 3rd International Workshop on Quantum Programming Languages},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0506134},
Keywords = {quantum computing; category theory; compact closed categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Coecke/De-linearizing Linearity Projective Quantum Axiomatics.pdf},
Title = {De-linearizing Linearity: Projective Quantum Axiomatics from Strong Compact Closure},
Year = {2005},
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@article{BellThe-Developemen,
Author = {Bell, J.L.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory; toposes; surveys},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Bell/The Developement of Categorical Logic.pdf},
Title = {The Developement of Categorical Logic},
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@article{Cuntz2001Quantum-Spaces-,
Author = {Cuntz, J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Notices of the AMS},
Keywords = {topology; quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Cuntz/Quantum Spaces and ther Noncommutative Topology.pdf},
Month = {September},
Pages = {793-799},
Title = {Quantum Spaces and ther Noncommutative Topology},
Year = {2001},
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@article{Scarani2005Quantum-Cloning,
Abstract = {The impossibility of perfectly copying (or cloning) an arbitrary quantum state is one of the basic rules governing the physics of quantum systems. The processes that perform the optimal approximate cloning have been found in many cases. These ''quantum cloning machines'' are important tools for studying a wide variety of tasks, e.g. state estimation and eavesdropping on quantum cryptography. This paper provides a comprehensive review of quantum cloning machines (both for discrete-dimensional and for continuous-variable quantum systems); in addition, it presents the role of cloning in quantum cryptography, the link between optimal cloning and light amplification via stimulated emission, and the experimental demonstrations of optimal quantum cloning. },
Author = {Scarani, V. and Iblisdir, S. and Gisin, N.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0511088},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Scarani/Quantum Cloning.pdf},
Title = {Quantum Cloning},
Year = {2005},
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@article{Oppenheim2005Uncommon-Inform,
Abstract = {If two parties share an unknown quantum state, one can ask how much quantum communication is needed for party A to send her share to party B. Recently, it was found that thenumber of qubits which should be sent is given by the conditional entropy. This quantifies the notion of partial information, and it can even be negative. Here, we not only demand that A send her state to B, but additionally, B should send his state to A. Paradoxically, we find that requiring that the parties perform this additional task can lower the amount of quantum communication required. This task, which we call quantum state exchange, can be used to quantify the notion of uncommon information, since the two parties only need to send each ot her the parts of their state they don't hold in common. In the classical case, the concept of uncommon information follows trivially from the concept of partial information. We find that for quantum states, this is not so. We prove upper and lower bounds for the uncommon information and find optimal protocols for several classes of states. },
Author = {Oppenheim, J. and Winter, A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0511082},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Oppenheim/Uncommon Information.pdf},
Title = {Uncommon Information},
Year = {2005},
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@misc{Alvarez-Gaume2005Introductory-Le,
Author = {{\'A}lvarez-Gaum{\'e}, L. and V{\'a}zquez-Mozo, M.A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0510040},
Howpublished = {Lecture Notes},
Keywords = {quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Álvarez-Gaumé/Introductory Lectures on Quantum Field Theory.pdf},
Organization = {3rd. CERN-CLAF School of High-Energy Physics},
Title = {Introductory Lectures on Quantum Field Theory},
Year = {2005},
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@article{Spiller2005Quantum-Computa,
Author = {Spiller, T.P. and Nemoto, K. and Braunstein, S.L. and Munro, W.J. and van Loock, P. and Milburn, G.J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0509202},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Spiller/Quantum Computation by Communication.pdf},
Title = {Quantum Computation by Communication},
Year = {2005},
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@article{Koike2005Demonstration-o,
Author = {Koike, S and Takahashi, H and Yonezawa, H and Takei, N. and Braunstein, S.L. and Aoki, T. and Furusawa, A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0507240},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Koike/Demonstration of quantum telecloning of optical coherent.pdf},
Title = {Demonstration of quantum telecloning of optical coherent states},
Year = {2005},
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@misc{KaroubiK-Theory:-An-el,
Author = {Karoubi, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Howpublished = {Lecture Notes},
Keywords = {topology},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Karoubi/K-Theory An elementary introduction.pdf},
Organization = {Clay Mathematics Research Academy},
Title = {K-Theory: An elementary introduction},
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@article{Aharonov2005A-polynomial-qu,
Author = {Aharonov, D and Jones, V. and Landau, Z.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0511096},
Keywords = {quantum computing; algorithms; topology},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Aharonov/A polynomial quatum algorithm for approximating the Jones.pdf},
Title = {A polynomial quatum algorithm for approximating the Jones polynomial},
Year = {2005},
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@inproceedings{Coecke2006Quantum-Measure,
Abstract = {Sums play a prominent role in the formalisms of quantum mechanics, be it for mixing and superposing states, or for composing state spaces. Surprisingly, a conceptual analysis of quantum measurement seems to suggest that quantum mechanics can be done without direct sums, expressed entirely in terms of the tensor product. The corresponding axioms define classical spaces as objects that allow copying and deleting data. Indeed, the information exchange between the quantum and the classical worlds is essentially determined by their distinct capabilities to copy and delete data. The sums turn out to be an implicit implementation of this capabilities. Realizing it through explicit axioms not only dispenses with the unnecessary structural baggage, but also allows a simple and intuitive graphical calculus. In category-theoretic terms, classical data types are dagger-compact Frobenius algebras, and quantum spectra underlying quantum measurements are Eilenberg-Moore coalgebras induced by these Frobenius algebras.},
Author = {Coecke, B. and Pavlovic, D.},
Booktitle = {The Mathematics of Quantum Computation and Technology},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Chen, G. and Kauffman, L. H. and Lomonaco, S.J., Jr},
Eprint = {quant-ph/0608035},
Keywords = {category theory; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Coecke/Quantum Measurements as coalgebras (or as pictures, if you prefer).pdf},
Publisher = {Taylor and Francis},
Series = {CRC Applied Mathematics \& Nonlinear Science},
Title = {Quantum Measurements without Sums},
Year = {2007},
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@article{Vickers1995Toposes-Pour-Le,
Author = {Vickers, S.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Semantics Society Newsletter},
Keywords = {category theory; toposes},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Vickers/Toposes Pour Les Nuls.pdf},
Title = {Toposes Pour Les Nuls},
Volume = {4},
Year = {1995},
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@article{VickersToposes-Pour-Le,
Abstract = {Restriction to geometric logic can enable one to define topological structures and continuous maps without explicit reference to topologies. This idea is illustrated with some examples and used to explain toposes as generalized topological spaces. },
Author = {Vickers, S.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory; toposes},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Vickers/Toposes Pour Les Vraiment Nuls.pdf},
Title = {Toposes Pour Les Vraiment Nuls},
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@book{Barr1985Toposes-Triples,
Author = {Barr, M. and Wells, C.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory; toposes},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Barr/Toposes, Triples and Theories.pdf},
Publisher = {Springer-Verlag},
Title = {Toposes, Triples and Theories},
Year = {1985},
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@inproceedings{AbramskyRetracing-Some-,
Author = {Abramsky, S.},
Booktitle = {Proceedings of CONCUR'96},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Montanari, U. and Sassone, V.},
Keywords = {process algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Abramsky/Retracing Some Paths in Process Algebra.pdf},
Number = {1119},
Pages = {1-17},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {Retracing Some Paths in Process Algebra},
Year = {1996},
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@inproceedings{AbramskyProcess-Realiza,
Author = {Abramsky, S.},
Booktitle = {Foundations of Secure Computation},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Bauer, F.L. and Steinbruggen, R.},
Keywords = {linear logic; process algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Abramsky/Process Realizability.pdf},
Pages = {167-190},
Publisher = {IOS Press},
Title = {Process Realizability},
Year = {2000},
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@misc{Abramsky2002Introduction-to,
Author = {Abramsky, S.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Howpublished = {Lecture Notes},
Keywords = {game semantics},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Abramsky/Introduction to Games Semantics Notes for a course.pdf},
Month = {June},
Title = {Introduction to Games Semantics: Notes for a course at NASSLI 2002},
Year = {2002},
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@inproceedings{AbramskyConcurrent-Game,
Abstract = {A new concurrent form of game semantics is introduced. This overcomes the problems which had arisen with previous, sequential forms of game semantics in modelling Linear Logic. It also admits an elegant and robust formalization. A Full Completeness Theorem for MultiplicativeAdditive Linear Logic is proved for this semantics.},
Author = {Abramsky, S. and Melli{\`e}s, P.-A.},
Booktitle = {Logic in Computer Science, 1999. Proceedings. 14th Symposium on},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {game semantics; linear logic},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Abramsky/Concurrent Games and Full Completeness.pdf},
Title = {Concurrent Games and Full Completeness},
Year = {1999},
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Bdsk-Url-1 = {http://dx.doi.org/10.1109/LICS.1999.782638}}
@misc{GuttmanTrust-Managemen,
Abstract = {We show how to combine trust management theories with nonce-based cryptographic protocols. The strand space framework for protocol analysis is extended by associating formulas from a trust management logic with the transmit and receive actions of the protocol principals. The formula on a transmission is a guarantee; the sender must ensure that this formula is true before sending the message. The formula on a receive event is an assumption that the recipient may rely on in deducing future guarantee formulas. The strand space framework allows us to prove that a protocol is sound, in the sense that when a principal relies on a formula, another principal has previously guaranteed it. We explain the ideas in reference to a simple new electronic commerce protocol, in which a customer obtains a money order from a bank to pay a merchant to ship some goods. },
Author = {Guttman, J.D. and Thayer, F.J and Carlson, J.A. and Herzog, J.C. and Ramsdell, J.D. and Sniffen, B.T.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {process algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Guttman/Trust Management in Strand Spaces A Rely-Guarantee.pdf},
Organization = {MITRE Corporation},
Title = {Trust Management in Strand Spaces: A Rely-Guarantee Method},
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@misc{May2002Notes-on-Atiyah,
Abstract = {As an example of ``categorification'', I presented Atiyah's axioms [1] for a topological quantum field theory (TQFT) to undergraduates in the University of Chicago's summer 2002 REU. These notes are written for the use of the participants and to test my own understanding.The aim is just to make very categorically precise what the basic definitions are. Also, there are some details in Atiyah's original definition that are subsumed in the more recent and by now standard categorical definition, and it seemed worthwhile to present a comparison. I have in mind hitting TQFT's with infinite loop space machines, which may perhaps provide a little unusual motivation. However, these notes are written to be readable by the students attending the REU, although standard categorical background that was explained in the talks is not repeated here. Needless to say, we have very good students at Chicago!!! },
Author = {May, J.P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Howpublished = {Lecture Notes},
Keywords = {quantum theory; topology; category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/May/Notes on Atiyah's TQFTs.pdf},
Organization = {University of Chicago},
Title = {Notes on Atiyah's TQFTs},
Year = {2002},
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@inproceedings{LomonacoAn-Entangled-Ta,
Author = {{Lomonaco Jr}, S.J.},
Booktitle = {Symposia in Applied Mathematics},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Lomonaco/An Entangled Tale of Quantum Entanglement.pdf},
Organization = {AMS},
Title = {An Entangled Tale of Quantum Entanglement},
Year = {2001},
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@article{Citterio2001Classifying-Spa,
Abstract = {In this paper we show how collapsing schemes can give us information on the homotopy type of the classifying space of a small category, when this category is presentedby a complete rewrite system. },
Author = {Citterio, M.G.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Theory and Applications of Categories},
Keywords = {category theory; topology},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Citterio/Classifying Spaces of Categories and Term Rewriting.pdf},
Number = {5},
Pages = {92-105},
Title = {Classifying Spaces of Categories and Term Rewriting},
Volume = {9},
Year = {2001},
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@misc{RazExponential-Sep,
Author = {Raz, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing; complexity},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Raz/Exponential Separation of Quantum and Classical Communication.pdf},
Title = {Exponential Separation of Quantum and Classical Communication Complexity},
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@mastersthesis{Pastro2004SigmaPi-Polycat,
Abstract = {We present a process semantics for the purely additive fragment of linear logic in which formulas denote protocols and (equivalence classes of) proofs denote multichannel concurrent processes. The polycategorical model induced by this process semantics is shown to be equivalent to the free polycategory based on the syntax (i.e., it is full and faithfully complete). This establishes that the additive fragment of linear logic provides a semantics of concurrent processes. Another property of this semantics is that it gives a canonical representation of proofs in additive linear logic. },
Annote = {Arxiv version missing diagrams.},
Author = {Pastro, C.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:math.CT/0312422},
Keywords = {polycategories; process algebra; linear logic},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Pastro/\Sigma\Pi-Polycategories, Additive Linear Logic and Process.pdf},
Month = {April},
School = {University of Calgary},
Title = {\Sigma\Pi-Polycategories, Additive Linear Logic and Process Semantics},
Year = {2004},
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Bdsk-Url-1 = {http://www.cpsc.ucalgary.ca/pastroc/}}
@inproceedings{KauffmanQuantum-Topolog,
Author = {Kauffman, L.H.},
Booktitle = {Symposia in Applied Mathematics},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum theory; quantum computing; topology},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Kauffman/Quantum Topology and Quantum Computing.pdf},
Organization = {AMS},
Title = {Quantum Topology and Quantum Computing},
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@article{Gaubert2004Two-dimensional,
Abstract = {In the paper M{\'e}tayer (2001), M{\'e}tayer transforms multiplicative proof-structures into orientable surfaces with boundaries. He investigates the link between the topological complexity and the number of exchanges in a sequentialisation. The theorem he achieves is about a particular rule of exchange (transpositions by blocks). We complete his approach by showing that the topological complexity does not provide any information in other cases (arbitrary exchange, upper bound of the number of exchanges). Then, we show that, on the other hand, the surface associated to a proof-structure is the surface of minimal complexity on which the proof can be drawn without crossing and respecting the local orientation. },
Author = {Gaubert, C},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Mathematical Structures in Computer Science},
Keywords = {linear logic; proof-nets; topology},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Gaubert/Two-dimensional proof-structures and the exchange rule.pdf},
Pages = {73-96},
Title = {Two-dimensional proof-structures and the exchange rule},
Volume = {14},
Year = {2004},
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Bdsk-Url-1 = {http://dx.doi.org/10.1017/S0960129503004092}}
@electronic{Ekert2000Basic-Concepts-,
Author = {Ekert, A. and Hayden, P. and Inamori, H.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0011013},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Ekert/Basic Concepts in Quantum Information.pdf},
Title = {Basic Concepts in Quantum Information},
Year = {2000},
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@article{Birkhoff1936The-Logic-of-Qu,
Author = {Birkhoff, G. and von Neumann, J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Annals of Mathematics},
Keywords = {quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Birkhoff/The Logic of Quantum Mechanics.pdf},
Month = {October},
Number = {4},
Pages = {823-843},
Title = {The Logic of Quantum Mechanics},
Volume = {37},
Year = {1936},
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Bdsk-Url-1 = {http://links.jstor.org/sici?sici=0003-486X(193610)2:37:4%3C823:TLOQM%3E2.0CO;2-Z}}
@electronic{Cabello2001Bells-Theorem-w,
Author = {Cabello, A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0008085},
Keywords = {quantum computing; quantum theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Cabello/Bell's Theorem without inequalities and without.pdf},
Title = {Bell's Theorem without inequalities and without probabilities for two observers},
Year = {2001},
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@electronic{Higuchi2000How-entangled-c,
Abstract = {We describe a pure state of four qubits whose single-qubit density matrices are all maximally mixed and whose average entanglement as a system of two pairs of qubits appears to be maximal.},
Author = {Higuchi, A. and Sudbury, A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0005013},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Higuchi/How entangled can two couples get?.pdf},
Title = {How entangled can two couples get?},
Year = {2000},
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@unpublished{ReifQuantum-Informa,
Author = {Reif, J.H},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Reif/Quantum Information Processing Compression, Coding.pdf},
Note = {Invited talk at Data Compression Conference (DCC'98)},
Title = {Quantum Information Processing: Compression, Coding and Related Computations},
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Bdsk-Url-1 = {http://www.cs.duke.edu/~reif/paper/qsurvey.ps}}
@unpublished{Danos2005Pauli-Measureme,
Abstract = {Following a suggestion of Briegel, we show that a variant of the oneway model where one only allows X and Y one qubit measurements is approximately universal with respect to unitaries.},
Author = {Danos, V. and Kashefi, E.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing; ; measurement-based quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Danos/Pauli Measurements are Universal.pdf},
Month = {April},
Note = {manuscript},
Title = {Pauli Measurements are Universal},
Year = {2005},
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@article{Katis1997Bicategories-of,
Abstract = {The suspension-loop construction is used to define a process in a symmetric monoidal category. The algebra of such processes is that of symmetric monoidal bicategories. Processes in categories with products and in categories with sums are studied in detail, and in both cases the resulting bicategories of processes are equipped with operations called feedback. Appropriate versions of traced monoidal properties are verified for feedback, and a normal form theorem for expressions of processes is proved. Connections with existing theories of circuit design and computation are established via structure preserving homomorphisms. },
Author = {Katis, P. and Sabadini, N. and Walters, R.F.C.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Journal of Pure and Applied Algebra},
Keywords = {category theory; process algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Katis/Bicategories of Processes.pdf},
Pages = {141-178},
Title = {Bicategories of Processes},
Volume = {115},
Year = {1997},
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@misc{Carroll2001A-No-Nonsense-I,
Author = {Carroll, S.M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Howpublished = {Lecture Notes},
Keywords = {relativity},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Carroll/A No-Nonsense Introduction to General Relativity.pdf},
Organization = {University of Chicago},
Title = {A No-Nonsense Introduction to General Relativity},
Year = {2001},
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@article{Blute2000Feedback-for-li,
Abstract = {In the present paper, we develop the notion of a trace operator on a linearly distributive category, which amounts to essentially working within a subcategory (the core) which has the same sort of ``type degeneracy'' as a compact closed category. We also explore the possibility that an object may have several trace structures, introducing a notion of compatibility in this case. We show that if we restrict to compatible classes of trace operators, an object may have at most one trace structure (for a given tensor structure). We give a linearly distributive version of the ``geometry of interaction'' construction, and verify that we obtain a linearly distributive category in which traces become canonical. We explore the relationship between our notions of trace and \00fixpoint operators, and show that an object admits a fi\00xpoint combinator precisely when it admits a trace and is a cocommutative comonoid. This generalises an observation of Hyland and Hasegawa. },
Author = {Blute, R.F. and Cockett, J.R.B and Seely, R.A.G.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Journal of Pure and Applied Algebra},
Keywords = {category theory; compact closed categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Blute/Feedback for linearly distributive categories traces.pdf},
Pages = {27-69},
Title = {Feedback for linearly distributive categories: traces and fixpoints},
Volume = {154},
Year = {2000},
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@article{Barnum2001Monotones-and-I,
Author = {Barnum, H. and Linden, N.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {stacks.iop.org/JPhysA/34/6787},
Journal = {Journal of Physics A : mathematical and general},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Barnum/Monotones and Invariants for multi-particle quantum states.pdf},
Month = {August},
Pages = {6787-6805},
Title = {Monotones and Invariants for multi-particle quantum states},
Volume = {34},
Year = {2001},
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@article{Galvao2000Tripartite-Enta,
Abstract = {We establish relations between tripartite pure state entanglement and additivity properties of the bipartite relative entropy of entanglement. Our results pertain to the asymptotic limit of local manipulations on a large number of copies of the state. We show that additivity of the relative entropy would imply that there are at least two inequivalent types of asymptotic tripartite entanglement. The methods used include the application of some useful lemmas that enable us to analytically calculate the relative entropy for some classes of bipartite states.},
Author = {Galvao, E.F. and Plenio, M.B. and Virmani, S.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Journal of Physics A : mathematical and general},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Galvao/Tripartite Entanglement and Quantum Relative Entropy.pdf},
Pages = {8809-8818},
Title = {Tripartite Entanglement and Quantum Relative Entropy},
Volume = {33},
Year = {2000},
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@incollection{Cleve1999An-Introduction,
Abstract = {We give a basic overview of computational complexity, query complexity, and communication complexity, with quantum information incorporated into each of these scenarios. The aim is to provide simple but clear definitions, and to highlight the interplay between the three scenarios and currently-known quantum algorithms. },
Author = {Cleve, R.},
Booktitle = {Collected Papers on Quantum Computation and Quantum Information Theory},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Macchiavello, C. and Palma, G .M. and Zeilinger, A.},
Eprint = {arXiv:quant-ph/9906111},
Keywords = {quantum computing; complexity},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Cleve/An Introduction to Quantum Complexity Theory.pdf},
Publisher = {World Scientific},
Title = {An Introduction to Quantum Complexity Theory},
Year = {2000},
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@electronic{Vidal1999Entanglement-Mo,
Abstract = {In the context of quantifying entanglement we study those functions of a multipartite state which do not increase under the set of local transformations. A mathematical characterization of these monotone magnitudes is presented. They are then related to optimal strategies of conversion of shared states. More detailed results are presented for pure states of bipartite systems. It is shown that more than one measure are required simultaneously in order to quantify completely the non-local resources contained in a bipartite pure state, while examining how this fact does not hold in the so-called asymptotic limit. Finally, monotonicity under local transformations is proposed as the only natural requirement for measures of entanglement.},
Author = {Vidal, G.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/9807077},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Vidal/Entanglement Monotones.pdf},
Title = {Entanglement Monotones},
Year = {1999},
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@electronic{Loock2002Multipartite-En,
Abstract = {First, we show how the quantum circuits for generating and measuring multi-party entanglement of qubits can be translated to continuous quantum variables. We derive sufficient inseparability criteria for N-party continuous-variable states and discuss their applicability. Then, we consider a family of multipartite entangled states (multi-party multi-mode states with one mode per party) described by continuous quantum variables and analyze their properties. These states can be efficiently generated using squeezed light and linear optics. },
Author = {van Loock, P. and Braunstein, S.L.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0205068},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Loock/Multipartite Entanglement.pdf},
Title = {Multipartite Entanglement},
Year = {2002},
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@electronic{Brus2001Characterizing-,
Abstract = {Quantum entanglement is at the heart of many tasks in quantum information. Apart from simple cases (low dimensions, few particles, pure states), however, the mathematical structure of entangle\00ment is not yet fully understood. This tutorial is an introduction to our present knowledge about how to decide whether a given state is separable or entangled, how to characterize entanglement via witness operators, how to classify entangled states according to their usefulness (i.e. distillability), and how to quantify entanglement with appropriate measures. },
Author = {Bru{\ss}, D.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0110078},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Bruß/Characterizing Entanglement.pdf},
Title = {Characterizing Entanglement},
Year = {2001},
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@electronic{Terhal2001Detecting-Quant,
Abstract = {We review the criteria for separability and quantum entanglement, both in a bi\00partite as well as a multipartite setting. We discuss Bell inequalities, entanglement witnesses, entropic inequalities, bound entanglement and several features of mul\00tipartite entanglement. We indicate how these criteria bear on the experimental detection of quantum entanglement.},
Author = {Terhal, B.M},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0101032},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Terhal/Detecting Quantum Entanglement.pdf},
Title = {Detecting Quantum Entanglement},
Year = {2001},
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@electronic{Fattal2006Entanglement-in,
Abstract = {4 We define a multi-partite entanglement measure for stabilizer states, which can be computed efficiently from a set of generators of the stabilizer group. Our measure applies to qubits, qudits and continuous variables. },
Author = {Fattal, D and Cubitt, T.S. and Yamamoto, Y. Bravyi, S. and Chuang, I. L.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv.org:quant-ph/0406168},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Fattal/Entanglement in the stabilizer formalism.pdf},
Title = {Entanglement in the stabilizer formalism},
Year = {2004},
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@electronic{Horodecki-2001-mseqc,
Author = {Horodecki, M. and Horodecki, P. and Horodecki, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/0109124},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Horodecki/Mixed-state entanglement and quantum communication.pdf},
Title = {Mixed-state entanglement and quantum communication},
Year = {2001},
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@misc{Coecke2005Kindergarten-Qu,
Abstract = {These lecture notes survey some joint work with Samson Abramsky as it was presented by me at several conferences in the summer of 2005. It concerns `doing quantum mechanics using only pictures of lines, squares, triangles and diamonds'. This picture calculus can be seen as a very substantial extension of Dirac's notation, and has a purely algebraic counterpart in terms of so-called Strongly Compact Closed Categories (introduced by Abramsky and I in [3, 4]) which subsumes my Logic of Entanglement [11]. For a survey on the `what', the `why' and the `hows' I refer to a previous set of lecture notes [12, 13]. In a last section we provide some pointers to the body of technical literature on the subject. },
Author = {Coecke, B.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Howpublished = {Lecture Notes},
Keywords = {quantum computing; category theory; compact closed categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Coecke/Kindergarten Quantum Mechanics.pdf},
Title = {Kindergarten Quantum Mechanics},
Year = {2005},
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@article{Vidal2002Computable-Meas,
Abstract = {We present a measure of entanglement that can be computed effectively for any mixed state of an arbitrary bipartite system. We show that it does not increase under local manipulations of the system, and use it to obtain a bound on the teleportation capacity and on the distillable entanglement of mixed states. },
Author = {Vidal, G. and Werner, R.F.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev. A},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Vidal/Computable Measure of Entanglement.pdf},
Month = {February},
Number = {032314},
Title = {Computable Measure of Entanglement},
Volume = {65},
Year = {2002},
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@article{Scott2004Multipartite-en,
Author = {Scott, A.J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev. A},
Keywords = {quantum computing, entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Scott/Multipartite entanglement, quantum-error-correcting codes, and entangling.pdf},
Title = {Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolution},
Volume = {69},
Year = {2004},
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@article{Partovi2004Universal-Meaas,
Author = {Partovi, H.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum computing, entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Partovi/Universal Meaasure of Entanglement.pdf},
Number = {7},
Title = {Universal Measure of Entanglement},
Volume = {92},
Year = {2004},
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@article{Hein2004Multiparty-enta,
Author = {Hein, M and Eisert, J and Briegel, H.J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev. A},
Keywords = {quantum computing, entanglement; ; measurement-based quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Hein/Multiparty entanglement in graph states.pdf},
Title = {Multiparty entanglement in graph states},
Volume = {69},
Year = {2004},
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@article{BCST1996Natural-Deducti,
Author = {Blute, R.F. and Cockett, J.R.B and Seely, R.A.G. and Trimble, T.H.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Journal of Pure and Applied Algebra},
Keywords = {linear logic; category theory;},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Blute/Natural Deduction and Coherence for Weakly Distributive.pdf},
Pages = {229-296},
Title = {Natural Deduction and Coherence for Weakly Distributive Categories},
Volume = {113},
Year = {1996},
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@article{CockettSeely97Proof-Theory-fo,
Author = {Cockett, J.R.B and Seely, R.A.G.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Theory and Applications of Categories},
Keywords = {category theory; linear logic; proof-nets},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Cockett/Proof Theory for Full Intuitionistic Linear.pdf},
Number = {5},
Pages = {85-131},
Title = {Proof Theory for Full Intuitionistic Linear Logic Bilinear Logic and Mix Categories},
Volume = {3},
Year = {1997},
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@article{Velinov1988An-Algebraic-St,
Author = {Velinov, Y.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Theoretical Computer Science},
Keywords = {category theory},
Pages = {205--224},
Read = {Yes},
Title = {An Algebraic Structure for Derivations in Rewriting Systems},
Volume = {57},
Year = {1988}}
@incollection{Lambek1969Deductive-Syste,
Author = {Lambek, J.},
Booktitle = {Category Theory, Homology Theory and their Applications I},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1007/BFb0079385},
Editor = {Hilton, R. J.},
Keywords = {category theory},
Pages = {76--122},
Publisher = {Springer},
Read = {Yes},
Series = {Lecture Notes in Mathematics},
Title = {Deductive Systems and Categories (II)},
Volume = {87},
Year = {1969},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/BFb0079385}}
@misc{svetlichny-2006-,
Abstract = {We show that Coecke's compositionality theorem for quantum information flow follows by the universal property of tensor products from the case in which all relevant states are totally disentangled, for which the proof is almost trivial. With the same technique we deduce a PROP structure behind general multipartite quantum information processing and show that all such are equivalent to a canonical teleportation-type form. Some philosophical issues concerning quantum information are also touched upon.},
Author = {Svetlichny, G.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv.org:quant-ph/0601093},
Keywords = {quantum computing; category theory; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Svetlichny/Tensor Universality, Quantum Information Flow,.pdf},
Title = {Tensor Universality, Quantum Information Flow, Coecke's Theorem, and Generalizations},
Year = {2006},
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Bdsk-Url-1 = {http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:quant-ph/0601093}}
@article{raussendorf-2002-49,
Author = {Raussendorf, R. and Browne, D. E. and Briegel, H. J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv.org:quant-ph/0108118},
Journal = {Journal of Modern Optics},
Keywords = {quantum computing; ; measurement-based quantum computing},
Pages = {1299},
Title = {The one-way quantum computer - a non-network model of quantum computation},
Volume = {49},
Year = {2002},
Bdsk-Url-1 = {doi:10.1080/09500340110107487}}
@article{raussendorf-2003-68,
Abstract = {We give a detailed account of the one-way quantum computer, a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states. We prove its universality, describe why its underlying computational model is different from the network model of quantum computation and relate quantum algorithms to mathematical graphs. Further we investigate the scaling of required resources and give a number of examples for circuits of practical interest such as thecircuit for quantum Fourier transformation and for the quantum adder. Finally, we describe computation with clusters of finite size. },
Author = {Raussendorf, R. and Browne, D. E. and Briegel, H. J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv.org:quant-ph/0301052},
Journal = {Physical Review A},
Keywords = {quantum computing; ; measurement-based quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Raussendorf/Measurement-based quantum computation with cluster.pdf},
Number = {022312},
Title = {Measurement-based quantum computation with cluster states},
Volume = {68},
Year = {2003},
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Bdsk-Url-1 = {http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:quant-ph/0301052}}
@article{Raussendorf-2001,
Author = {Raussendorf, R. and Briegel, H. J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum computing; ; measurement-based quantum computing},
Pages = {5188-5191},
Title = {A One-Way Quantum Computer},
Volume = {86},
Year = {2001},
Bdsk-Url-1 = {http://link.aps.org/abstract/PRL/v86/p5188}}
@article{Zukowski1993Event-Ready-Det,
Author = {Zukowski, M. and Zeilinger, A. and Horne, M. A. and Ekert, A. K.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Zukowski/Event Ready Detectors Bell Experiment.pdf},
Month = {4290},
Number = {26},
Pages = {4287},
Title = {Event Ready Detectors Bell Experiment via Entanglement Swapping},
Volume = {71},
Year = {1993},
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Bdsk-Url-1 = {http://prola.aps.org/abstract/PRL/v71/i26/p4287_1}}
@article{Cockett-2000-linearbicats,
Author = {Cockett, J.R.B and Koslowski, J. and Seely, R.A.G.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Mathematical Structures in Computer Science},
Keywords = {category theory},
Number = {2},
Pages = {165-203},
Title = {Introduction to linear bicategories},
Volume = {10},
Year = {2000}}
@article{Szabo1975Polycategories,
Author = {Szabo, M.E},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Comm. Algebra},
Keywords = {category theory},
Pages = {663-689},
Title = {Polycategories},
Volume = {3},
Year = {1975}}
@article{Koslowski2003A-monadic-appro,
Author = {Koslowski, J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Electronic Notes in Theoretical Computer Science},
Keywords = {category theory},
Month = {February},
Pages = {193-218},
Title = {A monadic approach to polycategories},
Volume = {69},
Year = {2003}}
@webpage{aaronson:zoo:2005,
Author = {Aaronson, S. and Kuperberg, G.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {complexity},
Rating = {4},
Read = {Yes},
Title = {The Complexity Zoo},
Bdsk-Url-1 = {http://qwiki.caltech.edu/wiki/Complexity_Zoo}}
@phdthesis{Ekert:thesis:1991,
Author = {Ekert, A. K.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing},
School = {Oxford University},
Title = {Correlations in Quantum Optics},
Year = {1991}}
@inproceedings{Calco,
Abstract = {We study structures which have arisen in recent work by the present author and Bob Coecke on a categorical axiomatics for Quantum Mechanics; in particular, the notion of strongly compact closed category. We explain how these structures support a notion of scalar which allows quantitative aspects of physical theory to be expressed, and how the notion of strong compact closure emerges as a significant refinement of the more classical notion of compact closed category. We then proceed to an extended discussion of free constructions for a sequence of progressively more complex kinds of structured category, culminating in the strongly compact closed case. The simple geometric and combinatorial ideas underlying these constructions are emphasized. We also discuss variations where a prescribed monoid of scalars can be `glued in' to the free construction. },
Author = {Abramsky, S.},
Booktitle = {Proceedings of CALCO 2005},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Fiadeiro, J.},
Eprint = {arXiv:0910.2931},
Keywords = {category theory; compact closed categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Abramsky/Abstract Scalars, Loops, and Free Traced.pdf},
Pages = {1--31},
Rating = {4},
Read = {Yes},
Series = {Springer Lecture Notes in Computer Science},
Title = {Abstract Scalars, Loops, and Free Traced and Strongly Compact Closed Categories},
Volume = {3629},
Year = {2005},
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@inproceedings{ArrDow:osftc:2004,
Author = {Arrighi, P. and Dowek, G.},
Booktitle = {Proceedings of the 2nd International Workshop on Quantum Programming Languages, Turku Centre for Computer Science General Publication No. 33},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Selinger, Peter},
Keywords = {quantum computing; programming language},
Pages = {21--38},
Title = {Operational Semantics for Formal Tensorial Calculus},
Year = {2004}}
@article{Vedral:quantifyent:1997,
Author = {Vedral, V. and Plenio, M. B. and Rippin, M. A. and Knight, P. L.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum computing; entanglement},
Number = {12},
Pages = {2275--2279},
Title = {Quantifying Entanglement},
Volume = {78},
Year = {1997}}
@inproceedings{watrous:succinct:2000,
Author = {Watrous, J.},
Booktitle = {Proceedings of the 41st Annual Symposium on Foundations of Computer Science},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing},
Pages = {537-546},
Title = {Succinct quantum proofs for properties of finite groups},
Year = {2000},
Bdsk-Url-1 = {arXiv:cs.CC/0009002}}
@article{DVC:threequbits:2000,
Author = {{D\"{u}}r, W and Vidal, G. and Cirac, J.I.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev. A},
Keywords = {quantum computing, entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/D\"ur/Three qubits can be entangled in two inequivalent ways.pdf},
Number = {6},
Title = {Three qubits can be entangled in two inequivalent ways},
Volume = {62},
Year = {2000},
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@book{Hatcher:2002:algebraictopology,
Author = {Hatcher, A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {topology},
Publisher = {Cambridge University Press},
Title = {Algebraic Topology},
Year = {2002}}
@article{Abramsky:2005:apt,
Abstract = {We revise our Physical Traces paper [Abramsky and Coecke CTCS02] in the light of the results in [Abramsky and Coecke LiCS04]. The key fact is that the notion of a strongly compact closed category allows abstract notions of adjoint, bipartite projector and inner product to be defined, and their key properties to be proved. In this paper we improve on the definition of strong compact closure as compared to the one presented in [Abramsky and Coecke LiCS04]. This modification enables an elegant characterization of strong compact closure in terms of adjoints and a Yanking axiom, and a better treatment of bipartite projectors. },
Author = {Abramsky, S. and Coecke, B.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Theory and Applications of Categories},
Keywords = {quantum computing, category theory, compact closed categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Abramsky/Abstract Physical Traces.pdf},
Number = {6},
Pages = {111-124},
Rating = {5},
Read = {Yes},
Title = {Abstract Physical Traces},
Volume = {14},
Year = {2005},
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@article{VDdMV:fourqubits:2002,
Author = {Verstraete, D. and Dehaene, J. and De Moor, B. and Verschelde, H.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev. A},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Verstraete/Four qubits can be entangled in nine different.pdf},
Title = {Four qubits can be entangled in nine different ways},
Volume = {52},
Year = {2002},
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@misc{hardy:reasonable:2001,
Author = {Hardy, L.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Howpublished = {arXiv.org:quant-ph/0101012},
Keywords = {quantum theory},
Title = {Quantum Theory From Five Reasonable Axioms},
Year = {2001},
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@article{BV:quantumcomplexity:1997,
Author = {Bernstein, E. and Vazirani, U},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {SIAM Journal on Computing},
Keywords = {quantum computing; complexity},
Number = {5},
Pages = {1411-1473},
Title = {Quantum complexity theory},
Volume = {25},
Year = {1997},
Bdsk-Url-1 = {http://www.cs.berkeley.edu/~vazirani/bv.ps}}
@article{Spekkens:epistemictoy:2004,
Abstract = {We present a toy theory that is based on a simple principle: the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge. A wide variety of quantum phenomena are found to have analogues within this toy theory. Such phenomena include: the noncommutativity of measurements, interference, the multiplicity of convex decompositions of a mixed state, the impossibility of discriminating nonorthogonal states, the impossibility of a universal state inverter, the distinction between bi-partite and tri-partite entanglement, the monogamy of pure entanglement, no cloning, no broadcasting, remote steering, teleportation, dense coding, mutually unbiased bases, and many others. The diversity and quality of these analogies is taken as evidence for the view that quantum states are states of incomplete knowledge rather than states of reality. A consideration of the phenomena that the toy theory fails to reproduce, notably, violations of Bell inequalities and the existence of a Kochen-Specker theorem, provides clues for how to proceed with this research program.},
Author = {Spekkens, R. W.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1103/PhysRevA.75.032110},
Howpublished = {arXiv.org:quant-ph/0401052},
Journal = {Phys. Rev. A},
Keywords = {quantum theory},
Number = {032110},
Title = {In defense of the Epistemic view of quantum states: a toy model},
Volume = {75},
Year = {2007},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.75.032110}}
@article{blute:1993:llcd,
Author = {Blute, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Theoretical Computer Science},
Keywords = {linear logic, category theory, , coherence; proof-nets},
Pages = {3-41},
Title = {Linear Logic, Coherence and Dinaturality},
Volume = {115},
Year = {1993}}
@inproceedings{Kelly:1993:clubs,
Author = {Kelly, G.M.},
Booktitle = {Applications of Categories in Computer Science},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Fourman, M.P. and Johnstone, P.T. and Pitts, A.M.},
Keywords = {category theory, coherence, types},
Pages = {163-190},
Publisher = {Cambridge University Press},
Series = {London Mathematical Society Lecture Notes},
Title = {On Clubs and Data-Type Constructors},
Volume = {177},
Year = {1992}}
@article{Brassard:qcommcomplxty:2003,
Author = {Brassard, G.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Foundations of Physics},
Keywords = {quantum computing; complexity},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Brassard/Quantum communication complexity.pdf},
Number = {11},
Pages = {1593 - 1616},
Title = {Quantum communication complexity},
Volume = {33},
Year = {2003},
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@unpublished{dHP:leaderelection:2005,
Author = {D'Hondt, E. and Panangaden, P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing; entanglement; algorithms},
Title = {Leader Election and Distributed Consensus with Quantum Resources},
Year = {2005},
Bdsk-Url-1 = {http://rl.cs.mcgill.ca/~prakash/leader.pdf}}
@inproceedings{AGN:1996:IntCats,
Author = {Abramsky, S. and Gay, S. and Nagarajan, R.},
Booktitle = {Proceedings of the 1994 Marktoberdorf Summer School on Deductive Program Design},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Broy, M},
Keywords = {types; category theory; process algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Abramsky/Interaction Categories and the Foundations of Typed Concurrent.pdf},
Pages = {35-113},
Publisher = {Springer-Verlag},
Title = {Interaction Categories and the Foundations of Typed Concurrent Programming},
Year = {1996},
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@article{Joyal:1977:conwaygames,
Author = {Joyal, A},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Gazette des sciences math{\'e}matiques du Qu{\'e}bec},
Keywords = {game semantics; category theory},
Notes = {2003 English translation by Robin Houston, available from http://www.cs.man.ac.uk/~houstorx},
Number = {4},
Title = {Remarques sur la Th{\'e}ories des Jeux {\`a} deux personnes},
Volume = {1},
Year = {1977},
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@article{JS:1991:GeoTenCal1,
Author = {Joyal, A. and Street, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Advances in Mathematics},
Keywords = {category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Joyal/The Geometry of Tensor Categories I.pdf},
Pages = {55-113},
Title = {The Geometry of Tensor Categories I},
Volume = {88},
Year = {1991},
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@inproceedings{DanKas:determinism:2005,
Abstract = {We introduce a flow condition on one-way measurement patterns which guarantees globally deterministic behaviour. Dependent Pauli corrections are derived for all such patterns, which 1) equalise all computation branches, and 2) only depend on the underlying entanglement graph and its choice of inputs and outputs. The class of patterns having flow is stable under composition and tensorisation, and has unitary embeddings as realisations. The restricted class of patterns having both flow and reverse flow, supports an operation of adjunction, and has all and only unitaries as realisations. },
Author = {Danos, V. and Kashefi, E.},
Booktitle = {ERATO conference on Quantum Information Science 2005},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv.org:quant-ph/0506062},
Keywords = {quantum computing, ; measurement-based quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Danos/Determinism in the one-way model.pdf},
Title = {Determinism in the one-way model},
Year = {2005},
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Bdsk-Url-1 = {http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:quant-ph/0506062}}
@article{JS:1993:GeoTenCal1,
Author = {Joyal, A. and Street, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Advances in Mathematics},
Keywords = {category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Joyal/Braided Tensor Categories.pdf},
Pages = {20-78},
Title = {Braided Tensor Categories},
Volume = {102},
Year = {1993},
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Bdsk-Url-1 = {http://dx.doi.org/10.1006/aima.1993.1055}}
@inproceedings{Selinger:dagger:2005,
Abstract = {Dagger compact closed categories were recently introduced by Abramsky and Coecke, under the name ``strongly compact closed categories'', as an axiomatic framework for quantum mechanics. We present a graphical language for dagger compact closed categories, and sketch proof of its completeness for equational reasoning. We give a general construction, the CPM construction, which associates to each dagger compact closed category its ``category of completely positive maps'', and we show that the resulting category is again dagger compact closed. We apply these ideas to Abramsky and Coecke's interpretation of quantum protocols, and to D'Hondt and Panangaden's predicate transformer semantics. },
Author = {Selinger, P.},
Booktitle = {Proceedings of the 3rd International Workshop on Quantum Programming Languages},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory; quantum computing; compact closed categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Selinger/Dagger compact closed categories and completely.pdf},
Title = {Dagger compact closed categories and completely positive maps},
Year = {2005},
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Bdsk-Url-1 = {http://www.mathstat.dal.ca/~selinger/qpl2005/PDFS/09-Selinger.pdf}}
@inproceedings{Pedrix:ent-n-sep:2005,
Abstract = {As a first step toward a notion of quantum data structures, we introduce a typing system for reflecting entanglement and separability. This is presented in the context of classically controlled quantum computation where a classical program controls a sequence of quantum operations, i.e. unitary transformations and measurements acting on a quantum memory. Abstract models for such quantum computations are the Quantum Random Access Machine (QRAM [5]) and the Classically-Controlled Quantum Turing Machine (CQTM [9]). Several quantum programming languages follow this model [1,3,6,12,13]. Among them, the functional language defined by Valiron [15] is the basis for the language developed in this paper. This is work in progress. },
Author = {Perdrix, S.},
Booktitle = {Proceedings of the 3rd International Workshop on Quantum Programming Languages},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing; types; entanglement; programming language},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Perdrix/Quantum patterns and types for entanglement and separability.pdf},
Series = {Electronic Notes in Computer Science},
Title = {Quantum patterns and types for entanglement and separability},
Year = {2005},
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@inproceedings{StrLam:pnmllunits:2004,
Author = {Stra{\ss}burger, L. and Lamarche, F.},
Booktitle = {Computer Science Logic, CSL 2004},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic},
Pages = {145--159},
Publisher = {Springer-Verlag},
Series = {Lecture Notes in Computer Science},
Title = {On Proof Nets for Multiplicative Linear Logic with Units},
Volume = {Add data for field: volume},
Year = {2004},
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@inproceedings{AbrGayNag:SpecStruct:1995,
Author = {Abramsky, S. and Gay, S. and Nagarajan, R.},
Booktitle = {Logics for Concurrency: Structure vs Automata --- Proceedings of the Banff Higher Order Workshop},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Moller, F. and Birtwistle, G.},
Keywords = {types; process algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Abramsky/Specification Structures and Propostitions-as-Types for Concurrency.pdf},
Publisher = {Springer-Verlag Lecture Notes in Computer Science},
Title = {Specification Structures and Propositions-as-Types for Concurrency},
Year = {1995},
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@inproceedings{Valiron:QTyping:2004,
Author = {Valiron, B.},
Booktitle = {Proceedings of the 2nd International Workshop on Quantum Programming Languages, Turku Centre for Computer Science General Publication No. 33},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing; types; programming language},
Title = {Quantum typing},
Year = {2004},
Bdsk-Url-1 = {http://www.mathstat.dal.ca/~selinger/qpl2004/PDFS/11Valiron.pdf}}
@article{HylSch:gomll:2003,
Author = {Hyland, M. and Schalk, A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Theoretical Computer Science},
Keywords = {linear logic; category theory},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Hyland/Gluing and Orthogonalty for Models of Linear Logic.pdf},
Pages = {183--231},
Title = {Gluing and Orthogonality for Models of Linear Logic},
Volume = {294},
Year = {2003},
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@inproceedings{enkirch-2004,
Author = {Altenkirch, T. and Grattage, J.},
Booktitle = {Proceedings of Logic in Computer Science},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing; programming language; types},
Title = {A functional quantum programming language},
Year = {2005},
Bdsk-Url-1 = {http://www.cs.nott.ac.uk/~txa/publ/qml.pdf}}
@phdthesis{Duncan:thesis:2006,
Author = {Duncan, R},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing; types; category theory; programming language; proof-nets},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Duncan/Types for Quantum Computation.pdf},
School = {Oxford University},
Title = {Types for Quantum Computing},
Year = {2006},
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@article{JorPer:Unifying:2004,
Author = {Jorrand, P. and Perdrix, S.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Jorrand/Unifying Quantum Computation with Projective.pdf},
Note = {arxiv:quant-ph/0404125},
Title = {Unifying Quantum Computation with Projective Measurements Only and One-Way Quantum Computation},
Year = {2004},
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@article{CocSee:wdc,
Author = {Cockett, R. and Seely, R.A.G.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Journal of Pure and Applied Algebra},
Keywords = {category theory; proof-nets},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Cockett/Weakly Distributive Categories.pdf},
Number = {2},
Pages = {229--296},
Title = {Weakly Distributive Categories},
Volume = {113},
Year = {1997},
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@article{Nielsen:UniProj:2003,
Author = {Nielsen, M.A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1016/S0375-9601(02)01803-0},
Eprint = {arxiv:quant-ph/0108020},
Journal = {Phys. Lett. A},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Nielsen/Universal Quantum Computation Using Only.pdf},
Number = {96},
Title = {Universal Quantum Computation Using Only Projective Measurement, Quantum Memory, and Preparation of the 0 State},
Volume = {308},
Year = {2003},
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Bdsk-Url-1 = {http://dx.doi.org/10.1016/S0375-9601(02)01803-0}}
@phdthesis{Tan:thesis:1997,
Author = {Tan, A. M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic; proof-nets},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Tan/Full Completeness For Models Of Linear Logic.pdf},
School = {Cambridge University},
Title = {Full Completeness For Models Of Linear Logic},
Year = {1997},
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@article{MooNie:PllQC:2002,
Author = {Moore, C. and Nilsson, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {SIAM J. Comput.},
Keywords = {quantum computing},
Number = {3},
Pages = {799--815},
Title = {Parallel Quantum Computation and Quantum Codes},
Volume = {31},
Year = {2001}}
@inproceedings{Girard:multiplicatives:1987,
Author = {Girard, J.-Y.},
Booktitle = {Logic and Computer Science: New Trends and Applcations},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Lolli, G.},
Keywords = {linear logic; proof-nets},
Pages = {11-37},
Publisher = {Rendiconti del Seminario Mathematico dell'Universita e Politecnico di Torino},
Title = {Multiplicatives},
Year = {1987}}
@phdthesis{Loader:thesis:1994,
Author = {Loader, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic},
School = {St Hugh's College, Oxford},
Title = {Models of Lambda Calculi and Linear Logic: Structural, Equational and Proof-theoretic Characterisations},
Year = {1994}}
@article{ABP:nuclearideals:1999,
Author = {Abramsky, S. and Blute, R. and Panangaden, P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Journal of Pure and Applied Algebra},
Keywords = {category theory; compact closed categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Abramsky/Nuclear and trace ideals in tensored *-categories.pdf},
Pages = {3-47},
Title = {Nuclear and trace ideals in tensored *-categories},
Volume = {143},
Year = {1999},
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@inproceedings{Terui:BoolPN:2004,
Author = {Terui, K.},
Booktitle = {Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science: LICS 2004},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic; complexity; proof-nets},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Terui/Proof Nets and Boolean Circuits.pdf},
Publisher = {IEEE Computer Society},
Title = {Proof Nets and Boolean Circuits},
Year = {2004},
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@inproceedings{Grover:fast:1996,
Author = {Grover, L. K.},
Booktitle = {Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing; algorithms},
Pages = {212-219},
Publisher = {ACM},
Title = {A fast quantum mechanical algorithm for database search},
Year = {1996}}
@book{Mitchell:ThCat:1965,
Author = {Mitchell, B.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory},
Publisher = {Academic Press},
Title = {Theory of Categories},
Year = {1965}}
@inproceedings{AbrDun:CQLv1:2004,
Abstract = {We define a sequent calculus corresponding to the logic of strongly compact closed categories with biproducts. Based on this calculus, we define a proof-net syntax with a strongly normalising cut-elimination. This syntax encodes abstract qualitative and quantitative information about the behaviour of quantum processes. },
Annote = {This is the informal proceedings},
Author = {Abramsky, S. and Duncan, R.},
Booktitle = {Proceedings of the 2nd International Workshop on Quantum Programming Languages, Turku Centre for Computer Science General Publication No. 33},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Selinger, Peter},
Keywords = {quantum computing; compact closed categories; proof-nets},
Pages = {3--20},
Title = {A Categorical Quantum Logic},
Year = {2004},
Bdsk-Url-1 = {http://quasar.mathstat.uottawa.ca/~selinger/qpl2004/PDFS/02Abramsky-Duncan.pdf}}
@article{JozLin:roleentspeed:2002,
Author = {Jozsa, R. and Linden, N.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arxiv:quant-ph/020143},
Journal = {Proceedings of the Royal Society A},
Keywords = {quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Jozsa/On the role of entanglement in quantum computational speed-up.pdf},
Month = {June},
Pages = {2011--2032},
Title = {On the role of entanglement in quantum computational speed-up},
Urldate = {8 March 2002},
Volume = {459},
Year = {2003},
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@article{BDSW:mixqecc:1996,
Author = {Bennett, C. H. and DiVicenzo, D. P. and Smolin, J. A. and Wootters, W. K.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev. A},
Keywords = {quantum computing, entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Bennett/Mixed state entanglement and quantum error-correcting.pdf},
Pages = {3824-3851},
Title = {Mixed state entanglement and quantum error-correcting codes},
Volume = {54},
Year = {1996},
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@phdthesis{Gottesman:thesis:1997,
Author = {Gottesman, D.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:quant-ph/9705052},
Keywords = {quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Gottesman/Stabliser codes and quantum error correction.pdf},
School = {California Institute of Technology},
Title = {Stabliser codes and quantum error correction},
Year = {1997},
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@article{AHS:2002:GoILinComAlg,
Author = {Abramsky, S. and Haghverdi, E. and Scott, P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Mathematical Structures in Computer Science},
Keywords = {linear logic; compact closed categories; category theory},
Pages = {625-665},
Title = {Geometry of Interaction and Linear Combinatory Algebras},
Volume = {12},
Year = {2002}}
@article{LMPZ:perfectqecc:1996,
Author = {Laflamme, R. and Miquel, C. and Paz, J.P. and Zurek, W.H.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum computing},
Number = {1},
Pages = {198-201},
Title = {Perfect quantum error-correcting code},
Volume = {77},
Year = {1996}}
@book{MacLane:CatsWM:1971,
Author = {Mac Lane, S.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory},
Publisher = {Springer-Verlag},
Title = {Categories for the Working Mathematician (2nd Ed.)},
Year = {1997}}
@unpublished{FKW:simTFT:2000,
Author = {Freedman, M. H. and Kitaev, A. and Wang, Z.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing; topology},
Note = {arXiv:quant-ph/0001071},
Title = {Simulation of topological field theories by quantum computers},
Year = {2000}}
@book{Kock:TQFT:2003,
Author = {Kock, J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum theory; category theory; topology},
Publisher = {Cambridge University Press},
Title = {Frobenius Algebras and 2-D Topological Quantum Field Theories},
Year = {2003}}
@book{Papadimitriou:CC:1994,
Author = {Papadimitriou, C. H.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {complexity},
Publisher = {Addison-Wesley},
Title = {Computational Complexity},
Year = {1994}}
@misc{shirahata:1996:comclseq,
Abstract = {In this paper, we introduce the system CMLL of sequent calculus and establish its correspondence with compact closed categories. CMLL is equivalent in provability to the system MLL of classical linear logic with the tensor and par connectives identified. We show that the system allows a fairly simple cut-elimination, and the proofs in the system have a natural interpretation in compact closed categories. However, the soundness of the cut-elimination procedure in terms of the categorical interpretation is by no means evident. We answer to this question affirmatively and establish the soundness by using the coherence result on compact closed categories by Kelly and Laplaza. },
Author = {Shirahata, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory; compact closed categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Shirahata/A sequent calculus for compact closed categories.pdf},
Title = {A sequent calculus for compact closed categories},
Year = {1996},
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Bdsk-Url-1 = {http://www.fbc.keio.ac.jp/~sirahata/Research/cmll.pdf}}
@article{Atiyah:TQFTs:1989,
Author = {Atiyah, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Publ. Math IHES},
Keywords = {quantum theory; topology},
Pages = {175-186},
Title = {Topological quantum field theories},
Volume = {68},
Year = {1989}}
@incollection{SanZul:QuantProg:2000,
Author = {Sanders, J. and Zuliani, P.},
Booktitle = {Mathematics of Program Construction},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing; programming language},
Pages = {80-99},
Publisher = {Springer},
Series = {LNCS},
Title = {Quantum Programming},
Volume = {1837},
Year = {2000}}
@article{Metayer:homology:1994,
Author = {M{\'e}tayer, F.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Arch. Math. Logic},
Keywords = {linear logic; proof-nets; topology},
Pages = {169-188},
Title = {Homology of proof-nets},
Volume = {33},
Year = {1994}}
@phdthesis{Omer:thesis:2003,
Author = {{\"{O}}mer, B.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing; programming language},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Omer/Structured Quantum Programming.pdf},
Month = {May},
School = {TU Vienna},
Title = {Structured Quantum Programming},
Year = {2003},
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@article{JSV:TraMonCat:1996,
Author = {Joyal, A. and Street, R. and Verity, D.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Math. Proc. Camb. Phil. Soc.},
Keywords = {category theory; compact closed categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Joyal/Traced Monoidal Categories.pdf},
Number = {3},
Pages = {447-468},
Title = {Traced Monoidal Categories},
Volume = {119},
Year = {1996},
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Bdsk-Url-1 = {http://dx.doi.org/10.1017/S0305004100074272}}
@inproceedings{GayNag:CQP:2004,
Author = {Gay, S. J. and Nagarajan, R.},
Booktitle = {Proceedings of the 2nd International Workshop on Quantum Programming Languages, Turku Centre for Computer Science General Publication No. 33},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Selinger, Peter},
Keywords = {quantum computing; programming language; process algebra},
Title = {Communicating Quantum Processes},
Year = {2004},
Bdsk-Url-1 = {http://www.dcs.gla.ac.uk/~simon/publications/CQP.pdf}}
@inproceedings{LalJor:procalgq:2004,
Author = {Lalire, M. and Jorrand, P.},
Booktitle = {Proceedings of the 2nd International Workshop on Quantum Programming Languages, Turku Centre for Computer Science General Publication No. 33},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Selinger, Peter},
Keywords = {quantum computing; process algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Lalire/A process algebraic approach to concurrent and distributed.pdf},
Title = {A process algebraic approach to concurrent and distributed quantum computation: operational semantics},
Year = {2004},
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Bdsk-Url-1 = {http://quasar.mathstat.uottawa.ca/~selinger/qpl2004/PDFS/08Lalire-Jorrand.pdf}}
@techreport{Duncan:BellStateMLL:2004,
Abstract = {By considering an explicit model of MLL over a compact closed category we show that cut-free MLL proof-nets (without units) may be realised as entangled quantum states and cut-elimination may be implemented as entanglement exchange. },
Author = {Duncan, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Institution = {Oxford University Computing Laboratory},
Keywords = {quantum computing; linear logic; compact closed categories; types; programming language},
Number = {PRG-RR-04-18},
Title = {Believe it or not, Bell states are a model of Multiplicative linear Logic},
Year = {2004}}
@book{Milner:CCSbook:1989,
Address = {London},
Author = {Milner, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {process algebra},
Publisher = {Prentice Hall},
Title = {Communication and Concurrency},
Year = {1989}}
@incollection{Deligne:tannakiennes:1991,
Author = {Deligne, P.},
Booktitle = {Grothendieck Festschrift},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory; compact closed categories},
Pages = {111-194},
Publisher = {Birkhauser},
Title = {Cat\'{e}gories Tannakiennes},
Volume = {2},
Year = {1991}}
@book{Hoare:CSPbook:1986,
Author = {Hoare, C.A.R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {process algebra},
Publisher = {Prentice Hall},
Title = {Communicating Sequential Processes},
Year = {1986}}
@article{Soloviev:superpositions:1987,
Author = {Soloviev, S. V.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1016/0022-4049(87)90061-2},
Journal = {Journal of Pure and Applied Algebra},
Keywords = {category theory},
Title = {On Natural Transformations of Distinguished Functors and their Superpositions in Certain Closed Categories},
Volume = {47},
Year = {1987},
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@inproceedings{AbrCoe:CatSemQuant:2004,
Abstract = {We study quantum information and computation from a novel point of view. Our approach is based on recasting the standard axiomatic presentation of quantum mechanics, due to von Neumann[28], at a more abstract level, of compact closed categories with biproducts. We show how the essential structures found in key quantum information protocols such as teleportation[5], logic-gate teleportation [12], and entanglement swapping[29] can be captured at this abstract level. Moreover, from the combination of the ---apparently purely qualitative---structures of compact closure and biproducts there emerge `scalars' and a `Born rule'. This abstract and structural point of view opens up new possibilities for describing and reasoning about quantum systems. It also shows the degrees of axiomatic freedom: we can show what requirements are placed on the (semi)ring of scalars C(I,I), where C is the category and I is the tensor unit, in order to perform various protocols such as teleportation. Our formalism captures both the information-flow aspect of the protocols[8,9], and the branching due to quantum indeterminism. This contrasts with the standard accounts, in which the classical information flows are `outside' the usual quantum-mechanical formalism. We give detailed formal descriptions and proofs of correctness of the example protocols.},
Author = {Abramsky, Samson and Coecke, Bob},
Booktitle = {Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science: LICS 2004},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing; compact closed categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Abramsky/A categorical semantics of quantum protocols.pdf},
Pages = {415-425},
Publisher = {IEEE Computer Society},
Title = {A categorical semantics of quantum protocols},
Year = {2004},
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@techreport{MilJen:bigraphs:2004,
Author = {Milner, R. and Jensen, O. H.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Institution = {University of Cambridge Computer Laboratory},
Keywords = {process algebra},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Milner/Bigraphs and Mobile Processes.pdf},
Number = {UCAM-CL-TR-580},
Title = {Bigraphs and Mobile Processes},
Year = {2004},
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@article{BBCJW:1993:teleport,
Author = {Bennett, C. and Brassard, G. and Crepeau, C. and Jozsa, R. and Peres, A. and Wootters, W.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum computing; algorithms; entanglement},
Pages = {1895--1899},
Title = {Teleporting an unknown quantum state via dual classical and {EPR} channels},
Year = {1993}}
@techreport{SasSob:ConCtxtGRW:2004,
Author = {Sassone, V. and Sobocinski, P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Institution = {BRICS},
Keywords = {category theory},
Number = {RS-04-11},
Title = {Congruences for Contextual Graph-Rewriting},
Year = {2004},
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@article{KelLap:comcl:1980,
Author = {Kelly, G.M. and Laplaza, M.L.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Journal of Pure and Applied Algebra},
Keywords = {category theory; coherence; compact closed categories},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Kelly/Coherence for Compact Closed Categories.pdf},
Pages = {193-213},
Title = {Coherence for Compact Closed Categories},
Volume = {19},
Year = {1980},
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@inproceedings{BDER:AJMgames:1997,
Author = {Baillot, P. and Danos, V. and Ehrhard, T. and Regnier, L.},
Booktitle = {Proceedings of the 12th Symposium on Logic in Computer Science},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic; game semantics},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Baillot/Believe it or not, AJM's games model.pdf},
Publisher = {IEEE Computer Society Press},
Title = {Believe it or not, AJM's games model is a model of classical Linear Logic},
Year = {1997},
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@techreport{Knill:Pseudocode:1996,
Author = {Knill, E.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Institution = {Los Alamos National Laboratory},
Keywords = {quantum computing; programming language},
Number = {LAUR-96-2724},
Title = {Conventions for quantum pseudocode},
Year = {1996}}
@article{Girard:LinLog:1987,
Author = {Girard, J.-Y.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Theoretical Computer Science},
Keywords = {linear logic; proof-nets},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Girard/Linear Logic.pdf},
Number = {1},
Title = {Linear Logic},
Volume = {50},
Year = {1987},
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@book{Isham:QuantTheory:1995,
Author = {Isham, C. J.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum theory},
Publisher = {Imperial College Press},
Title = {Lectures on Quantum Theory: Mathematical and Structural Foundations},
Year = {1995}}
@article{AbrCoe:PhysTra:2002,
Author = {Abramsky, S. and Coecke, B.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Electronic Notes in Theoretical Computer Science},
Keywords = {quantum computing; compact closed categories},
Title = {Physical Traces: Quantum vs. Classical Information Processing},
Volume = {69},
Year = {2002}}
@article{AbrJag:GFCMLL:1992,
Author = {Abramsky, S. and Jagadeesan, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Journal of Symbolic Logic},
Keywords = {linear logic; game semantics},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Abramsky/Games and Full Completeness for Multiplicative Linear.pdf},
Note = {Conference version appeared in FSTTCS '92},
Number = {2},
Pages = {543-574},
Title = {Games and Full Completeness for Multiplicative Linear Logic},
Volume = {59},
Year = {1994},
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@article{AbrJag:NewFndGOI:1992,
Author = {Abramsky, S. and Jagadeesan, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Information and Computation},
Keywords = {linear logic; compact closed categories},
Note = {Conference version appeared in LiCS '92},
Number = {1},
Pages = {53-119},
Title = {New Foundations for the Geometry of Interaction},
Volume = {111},
Year = {1994}}
@article{Abramsky:CompInterpLL:1993,
Author = {Abramsky, S.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Theoretical Computer Science},
Keywords = {linear logic},
Number = {1-2},
Pages = {3-57},
Title = {Computational Interpretations of Linear Logic},
Volume = {111},
Year = {1993}}
@unpublished{Abramsky:GamesLL:2003,
Author = {Abramsky, S.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {game semantics; linear logic},
Note = {Unpublished lecture notes, available from http://web.comlab.ox.ac.uk/oucl/work/samson.abramsky/gsem/index.html},
Title = {Game Semantics},
Year = {2003}}
@book{AspLon:CatTypStruct:1991,
Author = {Asperti, A. and Longo, G.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory},
Note = {Available online from \texttt{ftp://ftp.ens.fr/pub/dmi/users/longo/CategTypesStructures}},
Publisher = {MIT Press},
Title = {Categories, Types and Structures},
Year = {1991}}
@inproceedings{BB:BB84:1984,
Address = {Bangalore, India},
Author = {Bennett, C. H. and Brassard, G.},
Booktitle = {Proc. IEEE International Conference on Computers, Systems and Signal Processing},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing},
Month = {December},
Organization = {IEEE},
Pages = {175-179},
Publisher = {IEEE, New York},
Title = {Quantum cryptography: Public key distribution and coin tossing},
Year = {1984}}
@incollection{BWZ:QuantDenseTele:2000,
Author = {Bouwmeester, D. and Weinfurter, H. and Zeilinger, A.},
Booktitle = {The Physics of Quantum Information},
Chapter = {3},
Crossref = {BEZ:PhysQuantInf:2000},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Pages = {49-92},
Title = {Quantum Dense Coding and Quantum Teleportation}}
@book{Barr:*-AutoCats:1979,
Author = {Barr, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory},
Publisher = {SpringerVerlag},
Series = {Lecture Notes in Mathematics},
Title = {$*$-Autonomous Categories},
Volume = {752},
Year = {1979}}
@article{Barr:*-AutoLL:1991,
Author = {Barr, M.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Mathematical Structures in Computer Science},
Keywords = {linear logic; category theory},
Pages = {159-178},
Title = {*-autonomous categories and linear logic},
Volume = {1},
Year = {1991}}
@article{Bennett:B92:1992,
Author = {Bennett, C. H.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum computing},
Number = {21},
Pages = {3121-3124},
Title = {Quantum cryptography using any two nonorthonormal states},
Volume = {68},
Year = {1992}}
@unpublished{BluPanSee:FockSpaceExp:1994,
Author = {Blute, R. and Panangaden, P. and Seely, R. A. G.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Blute/Fock Space A Model of Linear Exponential.pdf},
Title = {{Fock} Space: {A} Model of Linear Exponential Types},
Year = {1994},
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@unpublished{Blute:OttawaNotes:2003,
Author = {Blute, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic;},
Month = {June},
Note = {Unpublished lecture, Fields Institute Summer School, Ottawa},
Title = {Introduction to Linear Logic},
Year = {2003}}
@book{CLR:Algorithms:1990,
Author = {Cormen, T. H. and Leiserson, C. E. and Rivest, R. L.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {algorithms},
Publisher = {MIT Press},
Title = {Introduction to Algorithms},
Year = {1990}}
@article{DanReg:Multiplicatives:1989,
Author = {Danos, V. and Regnier, L.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Arch. Math. Logic},
Keywords = {linear logic; proof-nets},
Number = {3},
Pages = {181-203},
Title = {The Structure of Multiplicatives},
Volume = {28},
Year = {1989}}
@incollection{EGHIW:QuantCrypt:2000,
Author = {Ekert, A. and Gisin, N. and Huttner, B. and Inamori, H. and Wenfurter, H.},
Booktitle = {The Physics of Quantum Information},
Chapter = {2},
Crossref = {BEZ:PhysQuantInf:2000},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Pages = {15-48},
Title = {Quantum Cryptography}}
@article{EPR:QMcomplete:1935,
Author = {Einstein, A. and Polodsky, B. and Rosen, N.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev.},
Keywords = {quantum computing},
Title = {Can quantum-mechanical descriptions of reality be considered complete?},
Volume = {47},
Year = {1935}}
@article{Ekert:QuantCrptBell:1991,
Author = {Ekert, A. K.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phys. Rev. Lett.},
Keywords = {quantum computing},
Number = {6},
Pages = {1769-1782},
Title = {Quantum Cryptography based on {B}ell's theorem},
Volume = {67},
Year = {1991}}
@article{EkertJozsa:EntEnh:1998,
Author = {Ekert, A. and Jozsa, R.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Phil. Trans. Roy. Soc. London Ser A},
Keywords = {quantum computing; algorithms; entanglement},
Title = {Quantum Algorithms: Entanglement Enhanced Information Processing},
Volume = {356},
Year = {1998}}
@article{Feynman:SimPhys:1982,
Author = {Feynman, R. P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Int. J. Theor. Phys.},
Keywords = {quantum computing; algorithms},
Number = {6/7},
Title = {Simulating Physics with Computers},
Volume = {21},
Year = {1982}}
@incollection{GRW:SrcEntPho:2000,
Author = {Gisin, N. and Rarity, J.G. and Weihs, G.},
Booktitle = {Physics of Quantum Information},
Chapter = {3.4},
Crossref = {BEZ:PhysQuantInf:2000},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Pages = {53-60},
Title = {Sources of Entangled Photons},
Year = {2000}}
@book{GirLafTay:ProofsTypes:1989,
Author = {Girard, J.-Y. and Lafont, Y. and Taylor, P.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic; proof-nets},
Optnote = {Available online from \texttt{http://www.dcs.qmw.ac.uk/~pt/stable/Proofs+Types.html}},
Publisher = {Cambridge University Press},
Title = {Proofs and Types},
Year = {1989}}
@article{Girard:LLL:1996,
Author = {Girard, J.-Y.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Information and Computation},
Keywords = {linear logic},
Number = {2},
Pages = {175-204},
Title = {Light Linear Logic},
Volume = {143},
Year = {1998},
Bdsk-Url-1 = {citeseer.nj.nec.com/girard95light.html}}
@incollection{Girard:LLSynSem:1995,
Author = {Girard, J.-Y.},
Booktitle = {Advances in Linear Logic},
Crossref = {GirLafReg:AdvLinLog:1995},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic; proof-nets},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Girard/Linear Logic its syntax and semantics.pdf},
Title = {Linear Logic: its syntax and semantics},
Year = {1995},
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@incollection{Girard:ProofNets:1996,
Abstract = {The paper is mainly concerned with the extension of proof-nets to additives, for which the best known solution is presented. It proposes two cut-elimination procedures, the lazy one being in linear time. The solution is shown to be compatible with quantifiers, and the structural rules of exponentials are also accommodated. },
Author = {Girard, J.-Y.},
Booktitle = {Logic and Algebra},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Dekker, M.},
Keywords = {linear logic; proof-nets},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Girard/Proof-nets the parallel syntax for proof theory.pdf},
Title = {Proof-nets: the parallel syntax for proof theory},
Year = {1996},
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@book{Gruska:QuantComp:1999,
Author = {Gruska, Jozef},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing},
Publisher = {McGraw-Hill},
Title = {Quantum Computing},
Year = {1999}}
@inproceedings{HugVGla:AddProofNets:2003,
Author = {Hughes, D. and van Glabbeek, R.},
Booktitle = {Proc. Logic in Computer Science 2003},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic; proof-nets},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Hughes/Proof Nets for Unit-free Multiplicative-Additive Linear.pdf},
Organization = {IEEE},
Title = {Proof Nets for Unit-free Multiplicative-Additive Linear Logic},
Year = {2003},
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@incollection{Jozsa:EntQC:1997,
Author = {Jozsa, R.},
Booktitle = {The Geomtric Universe},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Hugget and Mason and Tod and Tsou and Woodhouse},
Keywords = {quantum computing; entanglement},
Publisher = {Oxford University Press},
Title = {Entanglement and Quantum Computing},
Year = {1998}}
@incollection{Jozsa:QuantAlg:2000,
Author = {Jozsa, R.},
Booktitle = {The Physics of Quantum Information},
Chapter = {4.2},
Crossref = {BEZ:PhysQuantInf:2000},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Pages = {104-126},
Title = {Quantum Algorithms}}
@article{Lafont:SLL:2002,
Author = {Lafont, Y.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Theoretical Computer Science},
Keywords = {linear logic; complexity},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Lafont/Soft Linear Logic.pdf},
Pages = {163-180},
Title = {Soft Linear Logic},
Volume = {318},
Year = {2004},
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@inproceedings{MaiTer:CompCompCutE:2003,
Author = {Mairson, H. G. and Terui, K.},
Booktitle = {Proceedings of ICTCS 2003},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic; complexity; proof-nets},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Mairson/On the Computational Complexity of Cut-Elimination in Linear Logic.pdf},
Month = {October},
Number = {2841},
Pages = {23--36},
Publisher = {Springer-Verlag},
Series = {Lecture Notes in Computer Science},
Title = {On the Computational Complexity of Cut-Elimination in Linear Logic},
Year = {2003},
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@book{NieChu:QuantComp:2000,
Author = {Nielsen, M. A. and Chuang, I. L.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing},
Publisher = {Cambridge University Press},
Title = {Quantum Computation and Quantum Information},
Year = {2000}}
@incollection{Seely:LL*-AutoCfCa:1989,
Author = {Seely, R. A. G.},
Booktitle = {Conference on Categories in Computer Science and Logic},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {category theory; linear logic},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Seely/Linear_logic_star_autonomous_categories_and_cofree.pdf},
Month = {June},
Pages = {371-382},
Series = {AMS Contemporary Mathematics},
Title = {Linear logic, *-autonomous categories and cofree algebras},
Volume = {92},
Year = {1989},
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@article{Shor:PolyTimeFact:1997,
Author = {Shor, P. W.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {SIAM J.Sci.Statist.Comput.},
Keywords = {quantum computing; algorithms},
Number = {5},
Title = {Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer},
Volume = {26},
Year = {1997}}
@book{Takeuti:ProofTheory:1987,
Author = {Takeuti, G.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {proof theory},
Publisher = {North-Holland Publishing},
Title = {Proof Theory},
Year = {1987}}
@book{Troelstra:LecturesLL:1991,
Address = {Stanford},
Author = {Troelstra, A. S.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {linear logic},
Publisher = {Centre for the Study of Languages and Information},
Series = {CSLI Lecture Notes},
Title = {Lectures on Linear Logic},
Volume = {29},
Year = {1991}}
@book{Young:IntroHilb:1988,
Author = {Young, N.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {Hilbert space},
Publisher = {Cambridge University Press},
Title = {An introduction to Hilbert space},
Year = {1988}}
@unpublished{vanTonder:lamcalcQC:2003,
Author = {van Tonder, A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing; types; programming language},
Note = {Available at http://arxiv.org/abs/quant-ph/0307150},
Title = {A Lambda Calculus for Quantum Computation}}
@incollection{RauBri:OnewayQC:2003,
Author = {Raussendorf, R. and Briegel, H. J.},
Booktitle = {Quantum Information Processing},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Leuchs, G. and Beth, T.},
Keywords = {quantum computing; ; measurement-based quantum computing},
Publisher = {Wiley},
Title = {Computational Model for the One-Way Quantum Computer: Concepts and Summary},
Year = {2003}}
@techreport{Coecke:LoE:2003,
Author = {Coecke, B.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Institution = {Oxford University Computing Laboratory},
Keywords = {category theory; quantum computing; entanglement},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Coecke/Logic of Entanglement.pdf},
Note = {Short version: arxiv:quant-ph/0402014},
Number = {PRG-RR-03-12},
Title = {Logic of Entanglement},
Year = {2003},
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@book{GirLafReg:AdvLinLog:1995,
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Girard, Jean-Yves and Lafont, Yves and Regnier, Laurent},
Keywords = {linear logic; logic; proof theory},
Publisher = {Cambridge University Press},
Series = {London Mathematical Society Lecture Notes},
Title = {Advances in Linear Logic},
Volume = {222},
Year = {1995}}
@incollection{girard91normal,
Address = {New York},
Author = {Girard, J.-Y. and Scedrov, A. and Scott, P. J.},
Booktitle = {Proceedings Workshop Logic from Computer Science, Berkeley, {CA}, {USA}, 13--17 Nov 1989},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Moschovakis, Y. N.},
Keywords = {; linear logic},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Girard/Normal Forms and Cut-Free Proofs as Natural.pdf},
Pages = {217--241},
Publisher = {Springer-Verlag},
Title = {Normal Forms and Cut-Free Proofs as Natural Transformations},
Volume = {21},
Year = {1991},
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@article{DanosV:meac,
Author = {Danos, Vincent and Kashefi, Elham and Panangaden, Prakash},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1145/1219092.1219096},
Eprint = {arXiv:quant-ph/0412135},
Journal = {Journal of ACM},
Keywords = {quantum computing; ; measurement-based quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Danos/The Measurement Calculus.pdf},
Number = {2},
Title = {The Measurement Calculus},
Volume = {54},
Year = {2007},
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@proceedings{DBLP:conf/tlca/1993,
Bibsource = {DBLP, http://dblp.uni-trier.de},
Booktitle = {TLCA},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Editor = {Bezem, Marc and Groote, Jan Friso},
Isbn = {3-540-56517-5},
Keywords = {lambda calculus},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {Typed Lambda Calculi and Applications, International Conference on Typed Lambda Calculi and Applications, TLCA '93, Utrecht, The Netherlands, March 16-18, 1993, Proceedings},
Volume = {664},
Year = {1993}}
@book{BEZ:PhysQuantInf:2000,
Author = {Bouwmeester, D. and Ekert, A. and Zeilinger, A. (Eds.)},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {quantum computing},
Publisher = {Springer},
Title = {The Physics of Quantum Information},
Year = {2000}}
@article{barz2012demonstration,
Author = {Barz, Stefanie and Kashefi, Elham and Broadbent, Anne and Fitzsimons, Joseph F and Zeilinger, Anton and Walther, Philip},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Science},
Number = {6066},
Pages = {303--308},
Publisher = {American Association for the Advancement of Science},
Title = {Demonstration of blind quantum computing},
Volume = {335},
Year = {2012},
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@inproceedings{broadbent2009universal,
Author = {Broadbent, Anne and Fitzsimons, Joseph and Kashefi, Elham},
Booktitle = {Foundations of Computer Science, 2009. FOCS'09. 50th Annual IEEE Symposium on},
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Organization = {IEEE},
Pages = {517--526},
Title = {Universal blind quantum computation},
Year = {2009},
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@inproceedings{Danos:2007aa,
Abstract = {Modelling is becoming a necessity in studying biological signalling pathways, because the combinatorial complexity of such systems rapidly overwhelms intuitive and qualitative forms of reasoning. Yet, this same combinatorial explosion makes the traditional modelling paradigm based on systems of differential equations impractical. In contrast, agent-based or concurrent languages, such as κ [1,2,3] or the closely related BioNetGen language [4,5,6,7,8,9,10], describe biological interactions in terms of rules, thereby avoiding the combinatorial explosion besetting differential equations. Rules are expressed in an intuitive graphical form that transparently represents biological knowledge. In this way, rules become a natural unit of model building, modification, and discussion. We illustrate this with a sizeable example obtained from refactoring two models of EGF receptor signalling that are based on differential equations [11,12]. An exciting aspect of the agent-based approach is that it naturally lends itself to the identification and analysis of the causal structures that deeply shape the dynamical, and perhaps even evolutionary, characteristics of complex distributed biological systems. In particular, one can adapt the notions of causality and conflict, familiar from concurrency theory, to κ, our representation language of choice. Using the EGF receptor model as an example, we show how causality enables the formalization of the colloquial concept of pathway and, perhaps more surprisingly, how conflict can be used to dissect the signalling dynamics to obtain a qualitative handle on the range of system behaviours. By taming the combinatorial explosion, and exposing the causal structures and key kinetic junctures in a model, agent- and rule-based representations hold promise for making modelling more powerful, more perspicuous, and of appeal to a wider audience.},
Author = {Vincent Danos and J{\'e}r{\^o}me Feret and Walter Fontana and Russell Harmer and Jean Krivine},
Booktitle = {CONCUR 2007 -- Concurrency Theory},
Citation_Abstract_Html_Url = {http://link.springer.com/chapter/10.1007/978-3-540-74407-8_3},
Citation_Author = {Jean Krivine},
Citation_Author_Institution = {{\'E}cole Polytechnique},
Citation_Doi = {10.1007/978-3-540-74407-8_3},
Citation_Firstpage = {17},
Citation_Inbook_Title = {CONCUR 2007 -- Concurrency Theory},
Citation_Isbn = {978-3-540-74407-8},
Citation_Language = {en},
Citation_Lastpage = {41},
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Citation_Publication_Date = {2007/01/01},
Citation_Publisher = {Springer Berlin Heidelberg},
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Citation_Title = {Rule-Based Modelling of Cellular Signalling},
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Series = {Lecture Notes in Computer Science},
Title = {Rule-Based Modelling of Cellular Signalling},
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@article{DBLP:journals/mscs/DanosHW13,
Author = {Vincent Danos and Russell Harmer and Glynn Winskel},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1017/S0960129512000114},
Journal = {Mathematical Structures in Computer Science},
Number = {2},
Pages = {272--289},
Title = {Constraining rule-based dynamics with types},
Volume = {23},
Year = {2013},
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@inproceedings{:2013ab,
Author = {Jonathan Hayman and Tobias Heindel},
Booktitle = {Foundations of Software Science and Computation Structures},
Citation_Abstract_Html_Url = {http://link.springer.com/chapter/10.1007/978-3-642-37075-5_1},
Citation_Author = {Tobias Heindel},
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Citation_Inbook_Title = {Foundations of Software Science and Computation Structures},
Citation_Isbn = {978-3-642-37075-5},
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Citation_Lastpage = {16},
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Citation_Title = {Pattern Graphs and Rule-Based Models: The Semantics of Kappa},
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Title = {Pattern Graphs and Rule-Based Models: The Semantics of Kappa},
Twitter:Card = {summary},
Twitter:Description = {Domain-specific rule-based languages to represent the systems of reactions that occur inside cells, such as Kappa and BioNetGen, have attracted significant recent interest. For these models, powerful},
Twitter:Image = {http://link.springer.com/static-content/covers/books/180/9783642370755.jpg},
Twitter:Site = {SpringerSBM},
Twitter:Title = {Pattern Graphs and Rule-Based Models: The Semantics of Kappa},
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Volume = {7794},
Year = {2013},
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@inproceedings{:2013aa,
Abstract = {We develop a new `thermodynamic' approach to stochastic graph-rewriting. The ingredients are a finite set of reversible graph-rewriting rules {\mathcal{G}} (called generating rules), a finite set of connected graphs {\mathcal{P}} (called energy patterns), and an energy cost function ϵ:→ℝ\epsilon:{\mathcal{P}}\to{\mathbb{R}} . The idea is that {\mathcal{G}} defines the qualitative dynamics by showing which transformations are possible, while {\mathcal{P}} and ε specify the long-term probability π of any graph reachable under {\mathcal{G}} . Given ,{\mathcal{G}}, {\mathcal{P}} , we construct a finite set of rules {\mathcal{G}}_{\mathcal{P}} which (i) has the same qualitative transition system as {\mathcal{G}} , and (ii) when equipped with suitable rates, defines a continuous-time Markov chain of which π is the unique fixed point. The construction relies on the use of site graphs and a technique of `growth policy' for quantitative rule refinement which is of independent interest. The `division of labour' between the qualitative and the long-term quantitative aspects of the dynamics leads to intuitive and concise descriptions for realistic models (see the example in {\S}4). It also guarantees thermodynamical consistency (aka detailed balance), otherwise known to be undecidable, which is important for some applications. Finally, it leads to parsimonious parameterizations of models, again an important point in some applications.},
Author = {Vincent Danos and Russ Harmer and Ricardo Honorato-Zimmer},
Booktitle = {CONCUR 2013 -- Concurrency Theory},
Citation_Abstract_Html_Url = {http://link.springer.com/chapter/10.1007/978-3-642-40184-8_27},
Citation_Author = {Ricardo Honorato-Zimmer},
Citation_Author_Institution = {University of Edinburgh},
Citation_Doi = {10.1007/978-3-642-40184-8_27},
Citation_Firstpage = {380},
Citation_Inbook_Title = {CONCUR 2013 -- Concurrency Theory},
Citation_Isbn = {978-3-642-40184-8},
Citation_Language = {en},
Citation_Lastpage = {394},
Citation_Pdf_Url = {http://link.springer.com/content/pdf/10.1007%2F978-3-642-40184-8_27.pdf},
Citation_Publication_Date = {2013/01/01},
Citation_Publisher = {Springer Berlin Heidelberg},
Citation_Springer_Api_Url = {http://api.springer.com/metadata/pam?q=doi:10.1007/978-3-642-40184-8_27&api_key=},
Citation_Title = {Thermodynamic Graph-Rewriting},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1007/978-3-642-40184-8_27},
Editor = {Pedro R. D'Argenio and Hern{\'a}n Melgratti},
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Pages = {380-394},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {Thermodynamic Graph-Rewriting},
Twitter:Card = {summary},
Twitter:Description = {We develop a new `thermodynamic' approach to stochastic graph-rewriting. The ingredients are a finite set of reversible graph-rewriting rules},
Twitter:Image = {http://link.springer.com/static-content/covers/books/952/9783642401848.jpg},
Twitter:Site = {SpringerSBM},
Twitter:Title = {Thermodynamic Graph-Rewriting},
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Volume = {8052},
Year = {2013},
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@article{Courcelle199012,
Abstract = {The notion of a recognizable set of finite graphs is introduced. Every set of finite graphs, that is definable in monadic second-order logic is recognizable, but not vice versa. The monadic second-order theory of a context-free set of graphs is decidable. },
Author = {Bruno Courcelle},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {http://dx.doi.org/10.1016/0890-5401(90)90043-H},
Issn = {0890-5401},
Journal = {Information and Computation},
Number = {1},
Pages = {12 - 75},
Title = {The monadic second-order logic of graphs. I. Recognizable sets of finite graphs},
Url = {http://www.sciencedirect.com/science/article/pii/089054019090043H},
Volume = {85},
Year = {1990},
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@book{Courcelle:2012aa,
Author = {Bruno Courcelle and Joost Engelfriet},
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Citation_Author = {org.cambridge.ebooks.online.book.Author@4c56fd5c},
Citation_Date = {2012},
Citation_Doi = {10.1017/CBO9780511977619},
Citation_Isbn = {9780511977619},
Citation_Title = {Graph Structure and Monadic Second-Order Logic},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1017/CBO9780511977619},
Number = {138},
Publisher = {Cambridge University Press},
Series = {Encyclopedia of Mathematics and its Applications},
Title = {Graph Structure and Monadic Second-Order Logic A Language-Theoretic Approach},
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@article{Loveridge:2014aa,
Abstract = {We report first steps towards elucidating the relationship between contextuality, measurement-based quantum computation (MBQC) and the non-classical logic of a topos associated with the computation. We show that in a class of MBQC, classical universality \emph{requires} non-classical logic, which is "consumed" during the course of the computation, therefore pinpointing another potential quantum computational resource.},
Author = {Leon Loveridge and Raouf Dridi and Robert Raussendorf},
Citation_Arxiv_Id = {1408.0745},
Citation_Author = {Raussendorf, Robert},
Citation_Date = {2014/08/04},
Citation_Online_Date = {2014/08/04},
Citation_Pdf_Url = {http://arxiv.org/pdf/1408.0745},
Citation_Title = {Non-classical logic of classically universal measurement-based quantum computation},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:1408.0745},
Title = {Non-classical logic of classically universal measurement-based quantum computation},
Year = {2014},
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@book{Ehrig:2006ab,
Author = {Hartmut Ehrig and Karsten Ehrig and Ulrike Prange and Gabriele Taentzer},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1007/3-540-31188-2},
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Publisher = {Springer Berlin Heidelberg},
Series = {Monographs in Theoretical Computer Science},
Title = {Fundamentals of Algebraic Graph Transformation},
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Year = {2006},
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@article{Dixon:2011fk,
Abstract = {String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. The distinguishing feature of these diagrams is that edges need not be connected to vertices at both ends, and these unconnected ends can be interpreted as the inputs and outputs of a diagram. In this paper, we give a concrete construction for string diagrams using a special kind of typed graph called an open-graph. While the category of open-graphs is not itself adhesive, we introduce the notion of a selective adhesive functor, and show that such a functor embeds the category of open-graphs into the ambient adhesive category of typed graphs. Using this functor, the category of open-graphs inherits "enough adhesivity" from the category of typed graphs to perform double-pushout (DPO) graph rewriting. A salient feature of our theory is that it ensures rewrite systems are "type-safe" in the sense that rewriting respects the inputs and outputs. This formalism lets us safely encode the interesting structure of a computational model, such as evaluation dynamics, with succinct, explicit rewrite rules, while the graphical representation absorbs many of the tedious details. Although topological formalisms exist for string diagrams, our construction is discreet, finitary, and enjoys decidable algorithms for composition and rewriting. We also show how open-graphs can be parametrised by graphical signatures, similar to the monoidal signatures of Joyal and Street, which define types for vertices in the diagrammatic language and constraints on how they can be connected. Using typed open-graphs, we can construct free symmetric monoidal categories, PROPs, and more general monoidal theories. Thus open-graphs give us a handle for mechanised reasoning in monoidal categories.},
Author = {Lucas Dixon and Aleks Kissinger},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1017/S0960129512000138},
Eprint = {arXiv:1011.4114},
Journal = {Math. Structures in Comp. Sci.},
Keywords = {monoidal categories; graphical calculi; category theory; logic; rewriting},
Number = {2},
Pages = {308-359},
Title = {Open Graphs and Monoidal Theories},
Volume = {23},
Year = {2013},
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Bdsk-Url-1 = {http://dx.doi.org/10.1017/S0960129512000138}}
@article{Denney2006341,
Abstract = {Motivated by the concerns of theorem-proving, we generalise the notion of proof tree to that of hierarchical proof tree. Hierarchical trees extend ordinary trees by adding partial order structure to the set of nodes: that allows us to visualise a node as a rectangle in the plane rather than as a point, letting us use the containment relation to express structure additional to that given by a tree. A hierarchical proof tree, or hiproof for short, is a hierarchical tree with nodes labelled by tactics. We motivate the details of our definition by reference to the behaviour of tactics in tactical theorem proving. We characterise the construction of the ordinary proof tree underlying a hierarchical proof tree as a left adjoint. We then analyse the notion of proof refinement with respect to hierarchy, and we give a characterisation of hiproofs that is more directly suited to implementation. },
Author = {Ewen Denney and John Power and Konstantinos Tourlas},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {http://dx.doi.org/10.1016/j.entcs.2005.11.063},
Issn = {1571-0661},
Journal = {Electronic Notes in Theoretical Computer Science},
Keywords = {tactical theorem proving},
Note = {Proceedings of the 21st Annual Conference on Mathematical Foundations of Programming Semantics (MFPS XXI) Mathematical Foundations of Programming Semantics \{XXI\}},
Number = {0},
Pages = {341 - 359},
Title = {Hiproofs: A Hierarchical Notion of Proof Tree},
Url = {http://www.sciencedirect.com/science/article/pii/S1571066106002003},
Volume = {155},
Year = {2006},
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@inproceedings{Arrighi:2012aa,
Author = {Pablo Arrighi and Gilles Dowek},
Booktitle = {Automata, Languages, and Programming (ICALP 2012)},
Citation_Abstract_Html_Url = {http://link.springer.com/chapter/10.1007/978-3-642-31585-5_9},
Citation_Author = {Gilles Dowek},
Citation_Author_Email = {gilles.dowek@inria.fr},
Citation_Author_Institution = {INRIA},
Citation_Doi = {10.1007/978-3-642-31585-5_9},
Citation_Firstpage = {54},
Citation_Inbook_Title = {Automata, Languages, and Programming},
Citation_Isbn = {978-3-642-31585-5},
Citation_Language = {en},
Citation_Lastpage = {66},
Citation_Pdf_Url = {http://link.springer.com/content/pdf/10.1007%2F978-3-642-31585-5_9.pdf},
Citation_Publication_Date = {2012/01/01},
Citation_Publisher = {Springer Berlin Heidelberg},
Citation_Springer_Api_Url = {http://api.springer.com/metadata/pam?q=doi:10.1007/978-3-642-31585-5_9&api_key=},
Citation_Title = {Causal Graph Dynamics},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1007/978-3-642-31585-5_9},
Format-Detection = {telephone=no},
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Pages = {54-66},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {Causal Graph Dynamics},
Twitter:Card = {summary},
Twitter:Description = {We extend the theory of Cellular Automata to arbitrary, time-varying graphs.},
Twitter:Image = {http://link.springer.com/static-content/covers/books/390/9783642315855.jpg},
Twitter:Site = {SpringerSBM},
Twitter:Title = {Causal Graph Dynamics},
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Volume = {7392},
Year = {2012},
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@book{Arrighi:2009ab,
Author = {Pablo Arrighi},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Publisher = {Universit{\'e} de Grenoble},
Title = {Quantum Cellular Automata},
Year = {2009},
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@inproceedings{Arrighi:2009aa,
Abstract = {We consider a graph with a single quantum system at each node. The entire compound system evolves in discrete time steps by iterating a global evolution UU. We require that this global evolution UU be unitary, in accordance with quantum theory, and that this global evolution UU be causal, in accordance with special relativity. By causal we mean that information can only ever be transmitted at a bounded speed, the speed bound being quite naturally that of one edge of the underlying graph per iteration of UU. We show that under these conditions the operator UU can be implemented locally; i.e. it can be put into the form of a quantum circuit made up with more elementary operators -- each acting solely upon neighbouring nodes. We take quantum cellular automata as an example application of this representation theorem: this analysis bridges the gap between the axiomatic and the constructive approaches to defining QCA. KEYWORDS: Quantum cellular automata, Unitary causal operators, Quantum walks, Quantum computation, Axiomatic quantum field theory, Algebraic quantum field theory, Discrete space-time.},
Author = {Pablo Arrighi and Vincent Nesme and Reinhard Werner},
Booktitle = {QIP 2010},
Citation_Arxiv_Id = {0711.3975},
Citation_Author = {Werner, Reinhard},
Citation_Date = {2007/11/26},
Citation_Online_Date = {2009/10/23},
Citation_Pdf_Url = {http://arxiv.org/pdf/0711.3975},
Citation_Title = {Unitarity plus causality implies localizability},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:0711.3975},
Title = {Unitarity plus causality implies localizability},
Year = {2009},
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@mastersthesis{Dam:996aa,
Author = {Wim van Dam},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
School = {Univeristy of Nijmegen},
Title = {Quantum Cellular Automata},
Year = {1996},
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@book{Key,
Author = {Author/Editor},
Publisher = {Publisher},
Title = {Title},
Year = {Year}}
@book{Jacobs:2012ab,
Author = {B. Jacobs},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Publisher = {Cambridge University Press},
Title = {Introduction to Coalgebra. Towards Mathematics of States and Observations},
Year = {2017}}
@book{JacobsCLTT,
Address = {Amsterdam},
Author = {B. Jacobs},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Number = {141},
Publisher = {North Holland},
Series = {Studies in Logic and the Foundations of Mathematics},
Title = {Categorical Logic and Type Theory},
Year = {1999}}
@book{Ceccherini-Silberstein:2010aa,
Author = {Ceccherini-Silberstein, Tullio, Coornaert, Michel},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Publisher = {Springer},
Series = {Monographs in Mathematics},
Title = {Cellular Automata and Groups},
Viewport = {width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=0},
Year = {2010},
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@article{Capretta2006437,
Abstract = {The concept of recursive coalgebra of a functor was introduced in the 1970s by Osius in his work on categorical set theory to discuss the relationship between wellfounded induction and recursively specified functions. In this paper, we motivate the use of recursive coalgebras as a paradigm of structured recursion in programming semantics, list some basic facts about recursive coalgebras and, centrally, give new conditions for the recursiveness of a coalgebra based on comonads, comonad-coalgebras and distributive laws of functors over comonads. We also present an alternative construction using countable products instead of cofree comonads. },
Author = {Venanzio Capretta and Tarmo Uustalu and Varmo Vene},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {http://dx.doi.org/10.1016/j.ic.2005.08.005},
Issn = {0890-5401},
Journal = {Information and Computation},
Keywords = {Distributive laws},
Note = {Seventh Workshop on Coalgebraic Methods in Computer Science 2004},
Number = {4},
Pages = {437 - 468},
Title = {Recursive coalgebras from comonads},
Url = {http://www.sciencedirect.com/science/article/pii/S0890540105001963},
Volume = {204},
Year = {2006},
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Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S0890540105001963},
Bdsk-Url-2 = {http://dx.doi.org/10.1016/j.ic.2005.08.005}}
@inproceedings{psgraph13,
Abstract = {Complex automated proof strategies are often difficult to extract, visualise, modify, and debug. Traditional tactic languages, often based on stack-based goal propagation, make it easy to write proofs that obscure the flow of goals between tactics and are fragile to minor changes in input, proof structure or changes to tactics themselves. Here, we address this by introducing a graphical language called PSGraph for writing proof strategies. Strategies are constructed visually by ``wiring together'' collections of tactics and evaluated by propagating goal nodes through the diagram via graph rewriting. Tactic nodes can have many output wires, and use a filtering procedure based on goal-types (predicates describing the features of a goal) to decide where best to send newly-generated sub-goals. In addition to making the flow of goal information explicit, the graphical language can fulfil the role of many tacticals using visual idioms like branching, merging, and feedback loops. We argue that this language enables development of more robust proof strategies and provide several examples, along with a prototype implementation in Isabelle.},
Author = {Gudmund Grov and Aleks Kissinger and Yuhui Lin},
Booktitle = {Logic for Programming, Artificial Intelligence, and Reasoning (LPAR-19)},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1007/978-3-642-45221-5_23},
Eprint = {arXiv:1302.6890},
Pages = {324-339},
Publisher = {Springer},
Series = {Lecture Notes in Computer Science},
Title = {A Graphical Language for Proof Strategies},
Volume = {8312},
Year = {2013},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/978-3-642-45221-5_23}}
@article{Oreshkov:2011aa,
Author = {Ognyan Oreshkov and Fabio Costa and \vCaslav Brukner},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arxiv:1105.4464},
Keywords = {Quantum physics; alternative physical models; causality},
Title = {Quantum correlations with no causal order},
Year = {2011},
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@inproceedings{Mellies:2014aa,
Abstract = {We establish that the local state monad introduced by Plotkin and Power is a monad with graded arities in the category [Inj,Set]. From this, we deduce that the local state monad is associated to a graded Lawvere theory L which is presented by generators and relations, depicted in the graphical language of string diagrams.},
Author = {Paul-Andr{\'e} Melli{\`e}s},
Booktitle = {RTA-TLCA 2014},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Keywords = {string diagrams},
Pages = {334--348},
Publisher = {Springer},
Title = {Local States in String Diagrams},
Volume = {8560},
Year = {2014},
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@article{Ranchin:2014aa,
Abstract = {We find a sufficient set of equations between quantum circuits from which we can derive any other equation between stabilizer quantum circuits. To establish this result, we rely upon existing work on the completeness of the graphical ZX language for quantum processes, a two-coloured logical calculus for multi-qubit systems. The complexity of the circuit equations, as opposed to the very intuitive reading of the much smaller number of ZX equations, advocates the latter for performing computations with quantum circuits.},
Author = {Andr{\'e} Ranchin and Bob Coecke},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Description = {We find a sufficient set of equations between quantum circuits from which we can derive any other equation between stabilizer quantum circuits. To establish this result, we rely upon existing work on the completeness of the graphical ZX language for quantum processes, a two-coloured logical calculus for multi-qubit systems. The complexity of the circuit equations, as opposed to the very intuitive reading of the much smaller number of ZX equations, advocates the latter for performing computations with quantum circuits.},
Doi = {10.1103/PhysRevA.90.012109},
Journal = {Phys. Rev. A},
Number = {012109},
Title = {Complete set of circuit equations for stabilizer quantum mechanics},
Viewport = {width=device-width},
Volume = {90},
Year = {2014},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevA.90.012109}}
@article{Miyazaki:2013aa,
Abstract = {In measurement-based quantum computation (MBQC), elementary quantum operations can be more parallelized than the quantum circuit model by employing a larger Hilbert space of graph states used as the resource. Thus MBQC can be regarded as a method of quantum computation where the temporal resource described by the depth of quantum operations can be reduced compared to the quantum circuit model by using the extra spatial resource described by graph states. To analyze the trade-off relationship of the spatial and temporal resources, we consider a method to obtain quantum circuit decompositions of general unitary transformations represented by MBQC on graph states with a certain underlying geometry called generalized flow. We present a method to translate any MBQC with generalized flow into quantum circuits without extra spatial resource. We also show an explicit way to unravel acausal gates that appear in the quantum circuit decomposition derived by a translation method presented in [V. Danos and E. Kashefi, Phys. Rev. A {\bf 74}, 052310 (2006)] and that represent an effect of the reduction of the temporal resource in MBQC. Finally, by considering a way to deterministically simulate these acausal gates, we investigate a general framework to analyze the trade-off between the spacial and temporal resources for quantum computation.},
Author = {Jisho Miyazaki and Michal Hajdu{\v s}ek and Mio Murao},
Citation_Arxiv_Id = {1310.4043},
Citation_Author = {Murao, Mio},
Citation_Date = {2013/10/15},
Citation_Online_Date = {2014/09/29},
Citation_Pdf_Url = {http://arxiv.org/pdf/1310.4043},
Citation_Title = {An analysis of the trade-off between spatial and temporal resources for measurement-based quantum computation},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {arXiv:1310.4043},
Title = {An analysis of the trade-off between spatial and temporal resources for measurement-based quantum computation},
Year = {2013},
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@article{Hoare:2009:VSI:1592434.1592439,
Author = {Hoare, C.A.R. and Misra, Jayadev and Leavens, Gary T. and Shankar, Natarajan},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1145/1592434.1592439},
Journal = {ACM Comput. Surv.},
Number = {4},
Pages = {22:1--22:8},
Title = {The Verified Software Initiative: A Manifesto},
Volume = {41},
Year = {2009},
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Bdsk-Url-1 = {http://doi.acm.org/10.1145/1592434.1592439},
Bdsk-Url-2 = {http://dx.doi.org/10.1145/1592434.1592439}}
@article{Walther:2005aa,
Annote = {10.1038/nature03347},
Author = {Walther, P. and Resch, K. J. and Rudolph, T. and Schenck, E. and Weinfurter, H. and Vedral, V. and Aspelmeyer, M. and Zeilinger, A.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1038/nature03347},
Journal = {Nature},
Number = {7030},
Pages = {169--176},
Title = {Experimental one-way quantum computing},
Volume = {434},
Year = {2005},
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Bdsk-Url-1 = {http://dx.doi.org/10.1038/nature03347}}
@article{PhysRevLett.99.120503,
Author = {Chen, Kai and Li, Che-Ming and Zhang, Qiang and Chen, Yu-Ao and Goebel, Alexander and Chen, Shuai and Mair, Alois and Pan, Jian-Wei},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1103/PhysRevLett.99.120503},
Issue = {12},
Journal = {Phys. Rev. Lett.},
Month = {Sep},
Numpages = {4},
Pages = {120503},
Publisher = {American Physical Society},
Title = {Experimental Realization of One-Way Quantum Computing with Two-Photon Four-Qubit Cluster States},
Url = {http://link.aps.org/doi/10.1103/PhysRevLett.99.120503},
Volume = {99},
Year = {2007},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.99.120503},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.99.120503}}
@article{PhysRevLett.113.200501,
Author = {Tame, M. S. and Bell, B. A. and Di Franco, C. and Wadsworth, W. J. and Rarity, J. G.},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.1103/PhysRevLett.113.200501},
Journal = {Phys. Rev. Lett.},
Number = {20},
Numpages = {6},
Title = {Experimental Realization of a One-Way Quantum Computer Algorithm Solving Simon's Problem},
Volume = {113},
Year = {2014},
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Bdsk-Url-1 = {http://link.aps.org/doi/10.1103/PhysRevLett.113.200501},
Bdsk-Url-2 = {http://dx.doi.org/10.1103/PhysRevLett.113.200501}}
@article{Kock:1999aa,
Abstract = {We prove that certain categories arising from atoms in a Grothendieck topos are themselves Grothendieck toposes. We also investigate enrichments of these categories over the base topos; there are in fact often two distinct enrichments.},
Author = {Anders Kock and Gonzalo E. Reyes},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Journal = {Theory and Applications of Categories},
Keywords = {category theory},
Number = {10},
Pages = {251-265},
Title = {Aspects of fractional exponent functors},
Volume = {5},
Year = {1999},
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Title = {On right adjoints to exponential functors},
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Journal = {Quantum Studies: Mathematics and Foundations},
Keywords = {Action; Quantum computation; Variational principles; Yang--Mills Lagrangian},
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Publisher = {Springer},
Title = {Action, quantum computation and the structure of the Yang--Mills Lagrangian},
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@article{Horsman:2014aa,
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Dc.Description = {Computing is a high-level process of a physical system. Recent interest in non-standard computing systems, including quantum and biological computers, has brought this physical basis of computing to the forefront. There has been, however, no consensus on how to tell if a given physical system is acting as a computer or not; leading to confusion over novel computational devices, and even claims that every physical event is a computation. In this paper, we introduce a formal framework that can be used to determine whether a physical system is performing a computation. We demonstrate how the abstract computational level interacts with the physical device level, in comparison with the use of mathematical models in experimental science. This powerful formulation allows a precise description of experiments, technology, computation and simulation, giving our central conclusion: physical computing is the use of a physical system to predict the outcome of an abstract evolution . We give conditions for computing, illustrated using a range of non-standard computing scenarios. The framework also covers broader computing contexts, where there is no obvious human computer user. We introduce the notion of a `computational entity', and its critical role in defining when computing is taking place in physical systems.},
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@article{Pironio:2014aa,
Abstract = {The correlations that admit a local hidden-variable model are described by a family of polytopes, whose facets are the Bell inequalities. The Clauser--Horne--Shimony--Holt (CHSH) inequality is the simplest such Bell inequality and is a facet of every Bell polytope. We investigate for which Bell polytopes the CHSH inequality is also the unique (non-trivial) facet. We prove that the CHSH inequality is the unique facet for all bipartite polytopes where at least one party has a binary choice of dichotomic measurements, irrespective of the number of measurement settings and outcomes for the other party. Based on numerical results, we conjecture that it is also the unique facet for all bipartite polytopes involving two measurements per party where at least one measurement is dichotomic. Finally, we remark that these two situations can be the only ones for which the CHSH inequality is the unique facet, i.e., any polytope that does not correspond to one of these two cases necessarily has facets that are not of the CHSH form. As a byproduct of our approach, we derive a new family of facet inequalities.},
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Dc.Description = {The correlations that admit a local hidden-variable model are described by a family of polytopes, whose facets are the Bell inequalities. The Clauser--Horne--Shimony--Holt (CHSH) inequality is the simplest such Bell inequality and is a facet of every Bell polytope. We investigate for which Bell polytopes the CHSH inequality is also the unique (non-trivial) facet. We prove that the CHSH inequality is the unique facet for all bipartite polytopes where at least one party has a binary choice of dichotomic measurements, irrespective of the number of measurement settings and outcomes for the other party. Based on numerical results, we conjecture that it is also the unique facet for all bipartite polytopes involving two measurements per party where at least one measurement is dichotomic. Finally, we remark that these two situations can be the only ones for which the CHSH inequality is the unique facet, i.e., any polytope that does not correspond to one of these two cases necessarily has facets that are not of the CHSH form. As a byproduct of our approach, we derive a new family of facet inequalities.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to `50 years of Bell's theorem'.},
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Description = {The correlations that admit a local hidden-variable model are described by a family of polytopes, whose facets are the Bell inequalities. The Clauser--Horne--Shimony--Holt (CHSH) inequality is the simplest such Bell inequality and is a facet of every Bell polytope. We investigate for which Bell polytopes the CHSH inequality is also the unique (non-trivial) facet. We prove that the CHSH inequality is the unique facet for all bipartite polytopes where at least one party has a binary choice of dichotomic measurements, irrespective of the number of measurement settings and outcomes for the other party. Based on numerical results, we conjecture that it is also the unique facet for all bipartite polytopes involving two measurements per party where at least one measurement is dichotomic. Finally, we remark that these two situations can be the only ones for which the CHSH inequality is the unique facet, i.e., any polytope that does not correspond to one of these two cases necessarily has facets that are not of the CHSH form. As a byproduct of our approach, we derive a new family of facet inequalities.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to `50 years of Bell's theorem'.},
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@inproceedings{Kissinger:2014ab,
Abstract = {Categorical quantum mechanics (CQM) and the theory of quantum groups rely heavily on the use of structures that have both an algebraic and co-algebraic component, making them well-suited for manipulation using diagrammatic techniques. Diagrams allow us to easily form complex compositions of (co)algebraic structures, and prove their equality via graph rewriting. One of the biggest challenges in going beyond simple rewriting-based proofs is designing a graphical language that is expressive enough to prove interesting properties (e.g. normal form results) about not just single diagrams, but entire families of diagrams. One candidate is the language of !-graphs, which consist of graphs with certain subgraphs marked with boxes (called !-boxes) that can be repeated any number of times. New !-graph equations can then be proved using a powerful technique called !-box induction. However, previously this technique only applied to commutative (or cocommutative) algebraic structures, severely limiting its applications in some parts of CQM and (especially) quantum groups. In this paper, we fix this shortcoming by offering a new semantics for non-commutative !-graphs using an enriched version of Penrose's abstract tensor notation.},
Author = {Aleks Kissinger and David Quick},
Booktitle = {Proceedings of QPL 2014},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Doi = {10.4204/EPTCS.172.5},
Editor = {Bob Coecke and Ichiro Hasuo and Prakash Panangaden},
Keywords = {categorical quantum mechanics; graphical calculi},
Pages = {56-67},
Series = {Electronic Proceedings in Theoretical Computer Science},
Title = {Tensors, !-graphs, and non-commutative quantum structures},
Volume = {172},
Year = {2014},
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Bdsk-Url-1 = {http://dx.doi.org/10.4204/EPTCS.172.5}}
@book{LeinsterHigher-Operads-,
Author = {Leinster, Tom},
Date-Added = {2015-01-16 00:04:47 +0000},
Date-Modified = {2015-01-16 00:04:48 +0000},
Eprint = {http://arxiv.org/abs/math.CT/0305049},
Keywords = {category theory},
Publisher = {Cambridge University Press},
Series = {London Mathematical Society},
Title = {Higher Operads, Higher Categories},
Year = {2003},
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@inproceedings{EPTCS171.5,
Author = {Duncan, Ross and Perdrix, Simon},
Booktitle = {Proceedings 10th International Workshop on Quantum Physics and Logic, Castelldefels (Barcelona), Spain, 17th to 19th July 2013},
Date-Added = {2015-01-14 18:15:36 +0000},
Date-Modified = {2015-01-15 11:51:53 +0000},
Doi = {10.4204/EPTCS.171.5},
Editor = {Coecke, Bob and Hoban, Matty},
Eprint = {arXiv:1307.7048},
Pages = {50-62},
Publisher = {Open Publishing Association},
Series = {Electronic Proceedings in Theoretical Computer Science},
Title = {Pivoting makes the ZX-calculus complete for real stabilizers},
Volume = {171},
Year = {2014},
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Bdsk-Url-1 = {http://dx.doi.org/10.4204/EPTCS.171.5}}
@inproceedings{DBLP:conf/fsttcs/TorreP12,
Author = {Salvatore {La Torre} and Gennaro Parlato},
Booktitle = {{IARCS} Annual Conference on Foundations of Software Technology and Theoretical Computer Science, {FSTTCS} 2012, December 15-17, 2012, Hyderabad, India},
Date-Added = {2015-01-13 14:45:03 +0000},
Date-Modified = {2015-01-14 11:06:22 +0000},
Doi = {10.4230/LIPIcs.FSTTCS.2012.173},
Pages = {173--184},
Title = {Scope-bounded Multistack Pushdown Systems: Fixed-Point, Sequentialization, and Tree-Width},
Year = {2012},
Bdsk-Url-1 = {http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2012.173}}
@inproceedings{Duncan:2013lr,
Abstract = {In this paper we give a partially mechanized proof of the correctness of Steane's 7-qubit error correcting code, using the tool Quantomatic. To the best of our knowledge, this represents the largest and most complicated verification task yet carried out using Quantomatic.},
Author = {Ross Duncan and Maxime Lucas},
Booktitle = {Proceedings 10th International Workshop on Quantum Physics and Logic (QPL 2013)},
Date-Added = {2015-01-13 14:45:03 +0000},
Date-Modified = {2015-10-10 08:39:01 +0000},
Doi = {10.4204/EPTCS.171.4},
Editor = {Bob Coecke and Matty Hoban},
Eprint = {arXiv:1306.4532},
Keywords = {quantum computing; automated reasoning; verification; categorical quantum mechanics; graphical calculi},
Pages = {33-49},
Series = {Electronic Proceedings in Theoretical Computer Science},
Title = {Verifying the {S}teane code with {Q}uantomatic},
Volume = {171},
Year = {2014},
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Bdsk-Url-1 = {http://dx.doi.org/10.4204/EPTCS.171.4}}
@inproceedings{Aleks-Kissinger:2012qy,
Abstract = {String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric representations of string diagrams, amenable to automated reasoning about diagrammatic theories via graph rewrite systems. In this extended abstract, we show how the power of such rewrite systems can be greatly extended by introducing pattern graphs, which provide a means of expressing infinite families of rewrite rules where certain marked subgraphs, called !-boxes ("bang boxes"), on both sides of a rule can be copied any number of times or removed. After reviewing the string graph formalism, we show how string graphs can be extended to pattern graphs and how pattern graphs and pattern rewrite rules can be instantiated to concrete string graphs and rewrite rules. We then provide examples demonstrating the expressive power of pattern graphs and how they can be applied to study interacting algebraic structures that are central to categorical quantum mechanics.},
Author = {Aleks Kissinger and Alex Merry and Matvey Soloviev},
Booktitle = {Proceedings 8th International Workshop on Developments in Computational Models (DCM 2012), Cambridge, United Kingdom, 17 June 2012},
Date-Added = {2015-01-13 14:45:03 +0000},
Date-Modified = {2015-01-14 18:05:43 +0000},
Doi = {10.4204/EPTCS.143.5},
Editor = {Benedikt L{\"o}we and Glynn Winskel},
Eprint = {arXiv:1204.6695},
Pages = {54--66.},
Series = {Electronic Proceedings in Theoretical Computer Science},
Title = {Pattern Graph Rewrite Systems},
Volume = {143},
Year = {2014},
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Bdsk-Url-1 = {http://dx.doi.org/10.4204/EPTCS.143.5}}
@article{gudmund:11a,
Author = {Grov, Gudmund and Michaelson, Greg},
Date-Added = {2015-01-13 14:45:03 +0000},
Date-Modified = {2015-01-14 18:26:22 +0000},
Doi = {10.1007/s10990-011-9067-y},
Journal = {Higher-Order and Symbolic Computation},
Number = {2},
Pages = {191-226},
Title = {Hume box calculus: robust system development through software transformation},
Volume = {23},
Year = {2011},
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Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10990-011-9067-y}}
@article{Hardy:2010aa,
Abstract = {In this paper we consider general probabilistic theories that pertain to circuits which satisfy two very natural assumptions. We provide a formalism that is local in the following very specific sense: calculations pertaining to any region of spacetime employ only mathematical objects associated with that region. We call this "formalism locality". It incorporates the idea that space and time should be treated on an equal footing. Formulations that use a foliation of spacetime to evolve a state do not have this property nor do histories-based approaches. An operation (see figure on left) has inputs and outputs (through which systems travel). A circuit is built by wiring together operations such that we have no open inputs or outputs left over. A fragment (see figure on right) is a part of a circuit and may have open inputs and outputs. We show how each operation is associated with a certain mathematical object which we call a "duotensor" (this is like a tensor but with a bit more structure). In the figure on the left we show how a duotensor is represented graphically. We can link duotensors together such that black and white dots match up to get the duotensor corresponding to any fragment. The figure on the right is the duotensor for the above fragment. Links represent summing over the corresponding indices. We can use such duotensors to make probabilistic statements pertaining to fragments. Since fragments are the circuit equivalent of arbitrary spacetime regions we have formalism locality. The probability for a circuit is given by the corresponding duotensorial calculation (which is a scalar since there are no indices left over). We show how to put classical probability theory and quantum theory into this framework. [Note: the abstract in the paper has pictures.]},
Author = {Hardy, Lucien},
Date-Added = {2015-01-13 14:45:03 +0000},
Date-Modified = {2015-01-14 16:41:06 +0000},
Doi = {10.1017/S0960129512000163},
Eprint = {arXiv:1005.5164v1},
Journal = {Mathematical Structures in Computer Science},
Keywords = {graphical calculi; alternative physical models; quantum theory},
Month = {April},
Number = {Special Issue 02},
Pages = {399-440},
Title = {A formalism-local framework for general probabilistic theories including quantum theory},
Volume = {23},
Year = {2013},
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@inproceedings{Browne:2009fr,
Abstract = {We prove that one-way quantum computations have the same computational power as quantum circuits with unbounded fan-out. It demonstrates that the one-way model is not only one of the most promising models of physical realisation, but also a very powerful model of quantum computation. It confirms and completes previous results which have pointed out, for some specific problems, a depth separation between the one-way model and the quantum circuit model. Since one-way model has the same computational power as unbounded quantum fan-out circuits, the quantum Fourier transform can be approximated in constant depth in the one-way model, and thus the factorisation can be done by a polytime probabilistic classical algorithm which has access to a constant-depth one-way quantum computer. The extra power of the one-way model, comparing with the quantum circuit model, comes from its classical-quantum hybrid nature. We show that this extra power is reduced to the capability to perform unbounded classical parity gates in constant depth.},
Author = {Browne, Dan E. and Kashefi, Elham and Perdrix, Simon},
Booktitle = {Theory of Quantum Computation, Communication, and Cryptography (TQC'10)},
Date-Added = {2015-01-13 14:45:03 +0000},
Date-Modified = {2015-01-15 21:45:30 +0000},
Editor = {van Dam, Wim and Kendon, VivienM. and Severini, Simone},
Eprint = {arXiv:0909.4673},
Keywords = {measurement-based quantum computing; complexity; quantum computing},
Local-Url = {/Users/kwb13215/Documents/Reading/Science/papers/Browne/Computational depth complexity of measurement-based quantum.pdf},
Pages = {35-46},
Publisher = {Springer Berlin Heidelberg},
Series = {Lecture Notes in Computer Science},
Title = {Computational depth complexity of measurement-based quantum computation},
Volume = {6519},
Year = {2011},
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@inproceedings{tinker14,
Abstract = {We introduce Tinker, a tool for designing and evaluating proof strategies based on proof-strategy graphs, a formalism previously introduced by the authors. We represent proof strategies as open-graphs, which are directed graphs with additional input/output edges. Tactics appear as nodes in a graph, and can be `piped' together by adding edges between them. Goals are added to the input edges of such a graph, and flow through the graph as the strategy is evaluated. Properties of the edges ensure that only the right `type' of goals are accepted. In this paper, we detail the Tinker tool and show how it can be integrated with two different theorem provers: Isabelle and ProofPower.},
Author = {Grov, Gudmund and Kissinger, Aleks and Lin, Yuhui},
Booktitle = {Proceedings Eleventh Workshop on User Interfaces for Theorem Provers (UITP 2014)},
Date-Added = {2015-01-13 14:45:03 +0000},
Date-Modified = {2015-01-14 18:11:45 +0000},
Doi = {10.4204/EPTCS.167.5},
Editor = {Christoph Benzm{\"u}ller and Bruno Woltzenlogel Paleo},
Eprint = {arXiv:1410.8217},
Pages = {23--34},
Series = {EPTCS},
Title = {Tinker, tailor, solver, proof},
Volume = {167},
Year = {2014},
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