Quantum picturalism

References

• von Neumann , J. 1932 . Mathematische Grundlagen der Quantenmechanik , Berlin : Springer-Verlag .
   Google Scholar
• Birkhoff , G. 1958 . von Neumann and lattice theory . Bull. Am. Math. Soc. , 64 : 50 – 56 .
   Google Scholar
• Rédei , M. 1997 . Why John von Neumann did not like the Hilbert space formalism of quantum mechanics (and what he liked instead) . Stud. Hist. Phil. Mod. Phys. , 27 : 493 – 510 .
   Google Scholar
• Birkhoff , G. and von Neumann , J. 1936 . The logic of quantum mechanics . Ann. Math. , 37 : 823 – 843 .
   Google Scholar
• Coecke , B. , Moore , D. J. and Wilce , A. 2000 . “ Operational quantum logic: an overview, in ” . In Current Research in Operational Quantum Logic: Algebras, Categories and Languages , 1 – 36 . Berlin : Springer . [arXiv: quant-ph/0008019]
   Google Scholar
• Bub , J. 1997 . Interpreting the Quantum World , Cambridge : Cambridge University Press .
   Google Scholar
• Peres , A. 1998 . Interpreting the quantum world . Stud. Hist. Phil. Mod. Phys. , 29 : 611 [arXiv:quant-ph/9711003]
   Google Scholar
• Bennett , C. H. , Brassard , G. , Crépeau , C. , Jozsa , R. , Peres , A. and Wooters , W. K. 1993 . Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels . Phys. Rev. Lett. , 70 : 1895 – 1899 .
   PubMed Web of Science ®Google Scholar
• Ekert , A. 1991 . Quantum cryptography based on Bell's theorem . Phys. Rev. Lett. , 67 : 661 – 663 .
   PubMed Web of Science ®Google Scholar
• http://en.wikipedia.org/wiki/Quantum cryptography
   Google Scholar
• Schrödinger , E. 1935 . Discussion of probability relations between separated systems . Proc. Cam. Phil. Soc. , 31 : 555 – 563 .
   Google Scholar
• http://en.wikipedia.org/wiki/Sequent calculus
   Google Scholar
• Girard , J.-Y. 1987 . Linear logic . Theor. Comp. Sc. , 50 : 1 – 102 . See also http://en.wikipedia.org/wiki/Linear logic
   Web of Science ®Google Scholar
• Dieks , D. G.B.J. 1982 . Communication by EPR devices . Phys. Lett. A , 92 : 271 – 272 .
   Web of Science ®Google Scholar
• Wootters , W. and Zurek , W. 1982 . A single quantum cannot be cloned . Nature , 299 : 802 – 803 .
   Web of Science ®Google Scholar
• http://en.wikipedia.org/wiki/No cloning theorem
   Google Scholar
• Pati , A. K. and Braunstein , S. L. 2000 . Impossibility of deleting an unknown quantum state . Nature , 404 : 164 – 165 .
   Web of Science ®Google Scholar
• Danos , V. and Reignier , L. 1989 . The structure of multiplicatives . Arch. Math. Logic , 28 : 181 – 203 .
   Google Scholar
• Duncan , R. W. Types for Quantum Computing D.Phil. thesis, University of Oxford, 2006
   Google Scholar
• Eilenberg , S. and MacLane , S. 1945 . General theory of natural equivalences . Trans. Am. Math. Soc. , 58 : 231 – 294 .
   Web of Science ®Google Scholar
• Coecke , B. 2006 . “ Introducing categories to the practicing physicist, in ” . In What is Category Theory? Advanced Studies in Mathematics and Logic 30 , 45 – 74 . Milan : Polimetrica Publishing .
   Google Scholar
• Baez , J. C. 2006 . “ Quantum quandaries: a category-theoretic perspective ” . In The Structural Foundations of Quantum Gravity , Edited by: Rickles , D. , French , S. and Saatsi , J. T. 240 – 266 . Oxford University Press . [arXiv:quant-ph/0404040]
   Google Scholar
• Coecke , B. and Paquette , E. O. 2009 . “ Categories for the practising physicist ” . In New Structures for Physics , Edited by: Coecke , B. Berlin : Springer Lecture Notes in Physics, Springer . [arXiv:0905.3010]
   Google Scholar
• Baez , J. and Stay , M. 2009 . “ Physics, topology, logic and computation: a Rosetta Stone ” . In New Structures for Physics , Edited by: Coecke , B. Berlin : Springer Lecture Notes in Physics, Springer .
   Google Scholar
• Abramsky , S. and Tzevelekos , N. 2009 . “ Introduction to categories and categorical logic ” . In New Structures for Physics , Edited by: Coecke , B. Berlin : Springer Lecture Notes in Physics, Springer .
   Google Scholar
• Selinger , P. 2009 . “ A survey of graphical languages for monoidal categories ” . In New Structures for Physics , Edited by: Coecke , B. Berlin : Springer Lecture Notes in Physics, Springer .
   Google Scholar
• Lawvere , F. W. and Schanuel , S. H. 1997 . Conceptual Mathematics: A First Introduction to Categories , Cambridge : Cambridge University Press .
   Google Scholar
• MacLane , S. 1998 . Categories for the Working Mathematician , 2nd ed. , Berlin : Springer-Verlag .
   Google Scholar
• Coecke , B. The logic of entanglement Research Report PRG-RR-03-12, 2003, arXiv:quant-ph/0402014 (8 page short version), http://web.comlab.ox.ac.uk/oucl/publications/tr/rr-03-12.html (full 160 page version)
   Google Scholar
• Gottesman , D. and Chuang , I. L. 1999 . Quantum teleportation is a universal computational primitive . Nature , 402 : 390 – 393 [arXiv:quant-ph/9908010] .
   Web of Science ®Google Scholar
• Żukowski , M. , Zeilinger , A. , Horne , M. A. and Ekert , A. K. 1993 . ‘Event-ready-detectors’ Bell experiment via entanglement swapping . Phys. Rev. Lett. , 71 : 4287 – 4290 .
   PubMed Web of Science ®Google Scholar
• Laforest , M. , Baugh , J. and Laflamme , R. 2006 . Time-reversal formalism applied to maximal bipartite entanglement: theoretical and experimental exploration . Phys. Rev. A , 73 : 032323 [arXiv:quant-ph/0510048]
   Web of Science ®Google Scholar
• Bénabou , J. 1963 . Categories avec multiplication . Compt. Rend. Séanc. Acad Sci. Paris , 256 : 1887 – 1890 .
   Google Scholar
• Haag , R. 1992 . Local Quantum Physics: Fields, Particles, Algebras , Berlin : Springer-Verlag .
   Google Scholar
• Joyal , A. and Street , R. 1991 . The geometry of tensor calculus I . Adv. Math. , 88 : 55 – 112 .
   Web of Science ®Google Scholar
• Abramsky , S. and Coecke , B. A categorical semantics of quantum protocols , in . Proceedings of 19th IEEE Conference on Logic in Computer Science, IEEE Press . Piscataway, NJ. pp. 415 – 425 . [arXiv:quant-ph/0402130]
   Google Scholar
• Selinger , P. 2007 . Dagger compact closed categories and completely positive maps . ENTCS , 170 : 139 – 163 .
   Google Scholar
• Coecke , B. Complete positivity without positivity and without compactness Research Report PRG-RR-07-05, 2007, http://web.comlab.ox.ac.uk/oucl/publications/tr/rr-07-05.html
   Google Scholar
• Joyal , A. , Street , R. and Verity , D. 1996 . Traced monoidal categories . Proc. Camb. Phil. Soc. , 119 : 447 – 468 .
   Web of Science ®Google Scholar
• Coecke , B. , Paquette , E. O. and Perdrix , S. 2008 . Bases in diagrammatic quantum protocols . ENTCS , 218 : 131 – 152 . [arXiv:0808.1037]
   Google Scholar
• Kelly , G. M. and Laplaza , M. L. 1980 . Coherence for compact closed categories . J. Pure Appl. Alg. , 19 : 193 – 213 .
   Web of Science ®Google Scholar
• Hasegawa , M. , Hofmann , M. and Plotkin , G. Finite dimensional vector spaces are complete for traced symmetric monoidal categories LNCS 4800, 2008, pp. 367–385
   Google Scholar
• Selinger , P. Finite dimensional Hilbert spaces are complete for dagger compact closed categories . Proceedings of the 5th International Workshop on Quantum Physics and Logic . Reykjavik, Iceland.
   Google Scholar
• Abramsky , S. 2009 . No-cloning in categorical quantum mechanics , Edited by: Semantic Techniques for Quantum Computation , Mackie , I. and Gay , S. Cambridge : Cambridge University Press . to appear. Available at http://www.cambridge.org/uk/catalogue.asp?isbn= 9780521513746
   Google Scholar
• Coecke , B. and Pavlovic , D. 2007 . “ Quantum measurements without sums ” . In Mathematics of Quantum Computing and Technology , Edited by: Chen , G. , Kauffman , L. and Lamonaco , S. 567 – 604 . Abingdon : Taylor and Francis . [arXiv:quant-ph/0608035]
   Google Scholar
• Coecke , B. , Pavlovic , D. and Vicary , J. A new description of orthogonal bases arXiv:0810.0812, 2008
   Google Scholar
• Coecke , B. and Paquette , E. O. 2008 . POVMs and Naimark's theorem without sums . ENTCS , 210 : 15 – 31 . arXiv:quant-ph/0608072
   Google Scholar
• Carboni , A. and Walters , R. F.C. 1987 . Cartesian bicategories I . J. Pure Appl. Alg. , 49 : 11 – 32 .
   Web of Science ®Google Scholar
• Lack , S. 2004 . Composing PROPs . Theor. Appl. Cat. , 13 : 147 – 163 .
   Google Scholar
• Coecke , B. , Paquette , E. O. and Pavlovic , D. 2009 . “ Classical and quantum structuralism ” . In Semantic Techniques for Quantum Computation , Edited by: Mackie , I. and Gay , S. Cambridge : Cambridge University Press . [arXiv:0904.1997]
   Google Scholar
• Coecke , B. and W. Duncan , R. Interacting quantum observables . Proceedings of the 35th International Colloquium on Automata, Languages and Programming, LNCS 5126 . pp. 298 – 310 . Berlin : Springer . [extended version: arXiv:0906.4725]
   Google Scholar
• Kraus , K. 1987 . Complementary observables and uncertainty relations . Phys. Rev. D , 35 : 3070 – 3075 .
   PubMed Web of Science ®Google Scholar
• Schwinger , J. 1960 . Unitary operator bases . Proc. Nat. Acad. Sci. USA , 46 : 570 – 579 .
   PubMed Web of Science ®Google Scholar
• Dür , W. , Vidal , G. and Cirac , J. I. 2000 . Three qubits can be entangled in two inequivalent ways . Phys. Rev. A , 62 : 062314
   Web of Science ®Google Scholar
• Nielsen , M. A. and Chuang , L. 2000 . Quantum Computation and Quantum Information , Cambridge : Cambridge University Press .
   Google Scholar
• Duncan , R. and Perdrix , S. Graphs States and the necessity of Euler Decomposition arXiv:0902.0500, 2009
   Google Scholar
• Raussendorf , R. , Browne , D. E. and Briegel , H.-J. 2003 . Measurement-based quantum computation on cluster states . Phys. Rev. A , 68 : 022312 [arXiv:quant-ph/ 0301052]
   Web of Science ®Google Scholar
• Coecke , B. , Edwards , B. and Spekkens , R. The group theoretic origin of non-locality for qubits web.comlab. ox.ac.uk/publications/publication3026-abstract.html
   Google Scholar
• Einstein , A. , Podolsky , B. and Rosen , N. 1935 . Can quantum-mechanical description of physical reality be considered complete? . Phys. Rev. , 47 : 777 – 780 .
   Google Scholar
• Bell , J. 1964 . On the Einstein Podolsky Rosen paradox . Physics , 1 : 195
   Google Scholar
• Aspect , A. , Dalibard , J. and Roger , G. 1982 . Experimental test of Bell's inequalities using time-varying analyzers . Phys. Rev. Lett. , 49 : 1804 – 1807 .
   Web of Science ®Google Scholar
• Greenberger , D. M. , Horne , M. A. , Shimony , A. and Zeilinger , A. 1990 . Bell's theorem without inequalities . Am. J. Phys. , 58 : 1131 – 1143 .
   Web of Science ®Google Scholar
• Spekkens , R. 2007 . Evidence for the epistemic view of quantum states: a toy theory . Phys. Rev. A , 75 : 032110
   Web of Science ®Google Scholar
• Coecke , B. and Edwards , B. Toy quantum categories arXiv:0808.1037, 2008
   Google Scholar
• Svetlichny , G. Tensor universality, quantum information flow, Coecke's theorem, and generalizations unpublised [arXiv:quant-ph/0601093]
   Google Scholar
• Coecke , B. 2005 . “ Kindergarten quantum mechanics, in ” . In Quantum Theory: Reconsiderations of the Foundations III , 81 – 98 [arXiv:quant-ph/0510032] . New York : AIP Press .
   Google Scholar
• Penrose , R. 1971 . Applications of negative dimensional tensor calculus, inCombinatorial Mathematics and its Applications , 221 – 244 . New York : Academic Press .
   Google Scholar
• Baez , J. C. and Dolan , J. 1995 . Higher-dimensional algebra and topological quantum field theory . J. Math. Phys. , 36 : 6073 – 6105 . [arXiv:q-alg/9503002]
   Web of Science ®Google Scholar
• Kuperberg , G. 1996 . Spiders for rank 2 Lie algebras . Comm. Math. Phys. , 180 : 109 – 115 . [arXiv:q-alg/9712003]
   Web of Science ®Google Scholar
• Fuchs , J. , Runkel , I. and Schweigert , C. 2002 . TFT construction of RCFT correlators I: Partition Functions . Nuc. Phys. B. , 646 : 353 – 497 [arXiv:hep-th/0204148] .
   Web of Science ®Google Scholar
• Morrison , S. E. A diagrammatic category for the representation theory of U_q(sl_n) Ph.D. thesis, University of California at Berkeley, 2007
   Google Scholar
• Baez , J. C. (1993–2009) . This weeks finds in mathematical physics 1–256 http://www.math.ucr.edu/home/baez/TWF.html – see also the n-category café: http://golem.ph.utexas.edu/category/
   Google Scholar
• Dixon , L. , Duncan , R. W. and Kissinger , A. http://dream.inf.ed.ac.uk/projects/quantomatic/
   Google Scholar
• Coecke , B. 2007 . De-linearizing linearity: projective quantum axiomatics from strong compact closure . ENTCS , 170 : 47 – 72 . [arXiv:quant-ph/0506134]
   Google Scholar
• Atiyah , M. 1989 . Topological quantum field theories . Inst. Hautes Études Sci. Publ. Math. , 68 : 175 – 186 .
   Google Scholar
• Kock , J. 2003 . Frobenius Algebras and 2D Topological Quantum Field Theories , Cambridge : Cambridge University Press .
   Google Scholar