Quantum information-flow, concretely, and axiomatically

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 5833, Issue , 2005, Pages 15-29

  Coecke, Bob ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Category Theory; Classical and Quantum Information flow; Quantum Entanglement

Indexed keywords

COMPUTER PROGRAMMING LANGUAGES; FORMAL LOGIC; IDENTIFICATION (CONTROL SYSTEMS); INFORMATION ANALYSIS; NETWORK PROTOCOLS;

CATEGORY THEORY; CLASSICAL AND QUANTUM INFORMATION FLOW; QAUNTUM TELEPORTATION; QUANTUM ENTANGLEMENT;

QUANTUM THEORY;

EID: 27744505949     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.620297     Document Type: Conference Paper

References (32)

1. Abramsky, S. (1996) Retracing some paths in process algebra. Proceedings 7th International Conference on Concurrency Theory, LNCS 1119, 1-17.
2. Abramsky, S. (2004) High-level methods for quantum computation and quantum information. Pleanary talk at 19th Annual IEEE Symposium on Logic in Computer Science (LiCS'04). Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, IEEE Computer Science Press, web.comlab.ox.ac.uk/ oucl/work/samson.abramsky/hlmqci.ps
3. Abramsky, S., Blute, R. and Panangaden, P. (1999) Nuclear and trace ideals in tensored *-categories. Journal of Pure and Applied Algebra 143, 3-47.
4. Abramsky, S. and Coecke, B. (2003) Physical traces: quantum vs. classical information processing. Electronic notes on Theoretical Computer Science 69. arXiv:cs/0207057
5. Abramsky, S. and Coecke, B. (2004) A categorical semantics of quantum protocols. Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science (LiCS'04), IEEE Computer Science Press, (extended version at arXiv:quant-ph/0402130)
6. Abramsky, S. and Coecke, B. (2004) Abstract physical traces. Theory and Applications of Categories (Categories in Computer Science 2002 post proceedings).
7. Baez, J. (2004) Quantum quandaries: a category-theoretic perspective. Structural Foundations of Quantum Gravity, eds. S. French, D. Rickles and J. Sahatsi, Oxford University Press. arXiv:quant-ph/0404040
8. Bainbridge, E. S. (1976) Feedback and generalized logic. Information and Control 31, 75-96.
9. Barr, M. (1979) *-Autonomous Categories. Lecture Notes in Mathematics 752, Springer-Verlag.
10. Bennet, C. H., Brassard, C., Crépeau, C., Jozsa, R., Peres, A. and Wooters, W. K. (1993) Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Physical Review Letters 70, 1895-1899.
11. Birkhoff, G. and von Neumann, J. (1936) The logic of quantum mechanics. Annals of Mathematics 37, 823-843.
12. Coecke, B. (2002) Quantum logic in intuitionistic perspective. Studia Logica 70, 353-382. arXiv:math.LO/0011208
13. Coecke, B. (2003) The logic of entanglement. An invitation. Research Report PRG-RR-03-12 Oxford University Computing Laboratory, web.comlab.ox.ac.uk/ oucl/publications/tr/rr-03-12.html
14. 13 with some additions)
15. Coecke, B., Moore, D.J. and Wilce, A., (2000) Operational Quantum Logic: An Overview. In: Current Research in Operational Quantum Logic: Algebras, Categories and Languages (eds. B. Coecke et al.), pp. 1-36, Kluwer Academic Publishers. (contains over 200 references) arXiv:quant-ph/0008019.
16. Girard, J.-Y. (1987) Linear logic. Theoretical Computer Science 50, 1-102.
17. Gottesman, D. and Chuang, I. L. (1999) Quantum teleportation is a universal computational primitive. Nature 402, 390-393. arXiv:quant-ph/9908010
18. Hellwig, K.-E. and Kraus, K. (1968,1970) Operations and measurents. Volume II in Communications in Mathematical Physics 16, 142-147.
19. Joyal, A., Street, R. and Verity, D. (1996) Traced monoidal categories. Proceedings of the Cambridge Philosophical Society 119, 447-468.
20. Kelly, G. M. (1972) An abstract approach to coherence. Lecture Notes in Mathematics 281, 106-147.
21. Kelly, G. M. and Laplaza, M. L. (1980) Coherence for compact closed categories. Journal of Pure and Applied Algebra 19, 193-213.
22. Lambek, J. (1958) The mathematics of sentence structure. American Mathematical Monthly 56, 154-169.
23. Lambek, J. (1968,1969) Deductive systems and categories. Volume II in Springer Lecture Notes in Mathematics 86, 76-122.
24. Mitchell, B. (1965) Theory of Categories. Academic Press.
25. Pati, A. K. and Braunstein, S. L. (2000) Impossibility of deleting an unknown quantum state. Nature 404, 164-165. arXiv:quant-ph/9911090
26. Piron, C. (1976) Foundations of Quantum Physics. W.A. Benjamin Inc.
27. Seely, R. A. G. (1998) Linear logic, *-autonomous categories and cofree algebras. Categories in Computer Science and Logic, Contemporary Mathematics 92, 371-382.
28. Varadarajan, V.S. (1968) The Geometry of Quantum Theory. Springer-Verlach.
29. von Neumann, J. (1932) Mathematische Grundlagen der Quantenmechanik. Springer-Verlag.
30. English translation (1955): Mathematical Foundations of Quantum Mechanics. Princeton University Press.
31. Wootters, W. and Zurek., W. (1982) A single quantum cannot be cloned. Nature 299, 802-803.
32. Żukowski, M., Zeilinger, A., Home, M. A. and Ekert, A. K. (1993) 'Event-ready-detectors' Bell experiment via entanglement swapping. Physical Review Letters 71, 4287-4290.