Informational derivation of quantum theory

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 84, Issue 1, 2011, Pages

  Chiribella, Giulio ^a   D'Ariano, Giacomo Mauro ^b   Perinotti, Paolo ^b  

^a PERIMETER INSTITUTE FOR THEORETICAL PHYSICS   (Canada)

^b INFN SEZIONE DI PAVIA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

DISTINGUISHABILITY;

DATA PROCESSING;

QUANTUM THEORY;

EID: 79961113495     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.84.012311     Document Type: Article

References (44)

1. D. Hilbert, J. von Neumann, and L. Nordheim, Math. Ann. MAANA3 0025-5831 10.1007/BF01451579 98, 1 (1928).
2. J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, 1932).
3. G. Birkhoff, in Lattice Theory, edited by, R. P. Dilworth, Proceedings of the Second Symposium in Pure Mathematics of the American Mathematical Society (American Mathematical Society, Providence, 1961).
4. G. Birkhoff and J. von Neumann, Ann. Math. ANMAAH 0003-486X 10.2307/1968621 37, 743 (1936).
5. G. W. Mackey, The Mathematical Foundations of Quantum Mechanics (W. A. Benjamin, New York, 1963).
6. J. M. Jauch and C. Piron, Helv. Phys. Acta 36, 837 (1963).
7. B. Coecke, D. Moore, and A. Wilce, Current Research in Operational Quantum Logic: Algebras, Categories, Languages, Fundamental theories of physics series (Kluwer Academic, Amsterdam, 2000).
8. G. Ludwig, Foundations of Quantum Mechanics (Springer, New York, 1983 and 1985), Vols 1 and 2.
9. W. K. Wootters and W. H. Zurek, Nature (London) NATUAS 0028-0836 10.1038/299802a0 299, 802 (1982).
10. D. Dieks, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(82)90084-6, 92, 271 (1982).
11. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.70.1895 70, 1895 (1993).
12. S. Wiesner, Sigact News SIGNDM 0163-5700 10.1145/1008908.1008920 15, 78 (1983).
13. C. H. Bennett and G. Brassard, Proceedings IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India (IEEE, New York, 1984), pp. 175-179.
14. A. K. Ekert, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.67.661 67, 661 (1991).
15. P. W. Shor, SIAM J. Comput. 0097-5397 10.1137/S0097539795293172 26, 1484 (1997).
16. L. Hardy, e-print arXiv: quant-ph/0101012.
17. B. Dakic and C. Bruckner, e-print arXiv: 0911.0695.
18. L. Masanes and M. Müller, e-print arXiv: 1004.1483v2.
19. G. M. D'Ariano, AIP Conf. Proc. APCPCS 0094-243X 10.1063/1.2158715 810, 114 (2006); (Pubitemid 44790003)
20. G. M. D'Ariano, AIP Conf. Proc. 0094-243X 10.1063/1.2219356 844, 101 (2006);
21. G. M. D'Ariano, AIP Conf. Proc. APCPCS 0094-243X 10.1063/1.2713449 889, 79 (2007);
22. Proceedings of the 8th International Conference on Quantum Communication, Measurement and Computing (NICT, Japan, 2007), p. 345.
23. G. M. D'Ariano, in Philosophy of Quantum Information and Entanglement, edited by, A. Bokulich, and, G. Jaeger, (Cambridge University Press, Cambridge, 2010).
24. J. A. Wheeler, in Complexity, Entropy, and the Physics of Information, edited by, W. Zurek, (Addison-Wesley, Redwood City, CA, 1990).
25. G. Chiribella, G. M. D'Ariano, and P. Perinotti, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.062348 81, 062348 (2010).
26. E. Schrödinger, Proc. Cambridge Philos. Soc. MPCPCO 0305-0041 10.1017/S0305004100013554 31, 555 (1935).
27. In fact, the equivalence of all purifications under local reversible transformations is tightly related to what seems the main point of Schrödinger's paper, namely that all possible ensembles of a mixed state can be "steered" by measurements on the purifying system. This property is an immediate consequence of the equivalence of all purifications.
28. W. Arveson, An Invitation to C*-Algebras (Springer, New York, 1976).
29. W. F. Stinespring, Proc. Am. Math. Soc. 10.1090/S0002-9939-1955-0069403-4 6, 211 (1955).
30. M. A. Nielsen and I. L. Chuang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.321 79, 321 (1997).
31. In quantum theory the trivial system I is represented by the one-dimensional Hilbert space HC.
32. B. Coecke, in Quantum Theory: Reconsiderations of the Foundations III (AIP, New York, 2005), p. 81.
33. B. Coecke, Contemp. Phys. CTPHAF 0010-7514 10.1080/00107510903257624 51, 59 (2010).
34. G. Chiribella, G. M. D'Ariano, and P. Perinotti, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/83/30004 83, 30004 (2008).
35. G. Chiribella, G. M. D'Ariano, and P. Perinotti, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.80.022339 80, 022339 (2009).
36. L. Hardy, J. Phys. A PLRAAN 1751-8113 10.1088/1751-8113/40/12/S12 40, 3081 (2007).
37. L. Hardy, e-print arXiv: 1005.5164.
38. B. Coecke and R. Lal, in Proceedings of the 7th workshop on Quantum Physics and Logic, edited by, B. Coecke, P. Panangaden, and, P. Selinger, [http://www.cs.ox.ac.uk/people/bob.coecke/QPL-proceedings.html] (unpublished).
39. J. Barrett, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.032304 75, 032304 (2007). (Pubitemid 46375513)
40. A. Wilce, Found. Phys. FNDPA4 0015-9018 10.1007/s10701-010-9410-x 40, 434 (2010).
41. L. Hardy and W. K. Wootters, e-print arXiv: 1005.4870.
42. D. Deutsch, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.44.3197 44, 3197 (1991).
43. C. H. Bennett, D. Leung, G. Smith, and J. A. Smolin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.170502 103, 170502 (2009).
44. G. Chiribella, G. M. D'Ariano, and P. Perinotti (in preparation).