Relaxed Bell inequalities and Kochen-Specker theorems

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 84, Issue 2, 2011, Pages

  Hall, Michael J W ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

BELL INEQUALITIES; DETERMINISTIC MODELS; FREE WILL; KOCHEN-SPECKER THEOREM; QUANTITATIVE COMPARISON; QUANTUM CORRELATIONS;

INFORMATION THEORY;

BELLS;

EID: 79961058862     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.84.022102     Document Type: Article

References (50)

1. J. S. Bell, Physics 1, 195 (1964).
2. J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.23.880 23, 880 (1969).
3. See, e.g., M. Zukowski and C. Brukner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.210401 88, 210401 (2002);
4. E. G. Cavalcanti, C. J. Foster, M. D. Reid, and P. D. Drummond, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.210405 99, 210405 (2007). (Pubitemid 350159236)
5. See, e.g., J. A. Clauser and M. A. Horne, Phys. Rev. D PRVDAQ 1550-7998 10.1103/PhysRevD.10.526 10, 526 (1974);
6. T. Norsen, Found. Phys. FNDPA4 0015-9018 10.1007/s10701-009-9281-1 39, 273 (2009).
7. See, e.g., S. L. Braunstein and C. M. Caves, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.61.662 61, 662 (1988);
8. B. W. Schumacher, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.44.7047 44, 7047 (1991).
9. D. Collins and N. Gisin, J. Phys. A 0305-4470 10.1088/0305-4470/37/5/021 37, 1775 (2004). (Pubitemid 38214186)
10. S. Kochen and E. P. Specker, J. Math. Mech. 17, 59 (1967).
11. J. S. Bell, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.38.447 38, 447 (1966).
12. P. Heywood and M. L. G. Redhead, Found. Phys. FNDPA4 0015-9018 10.1007/BF00729511 13, 481 (1983).
13. N. D. Mermin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.65. 3373 65, 3373 (1990).
14. L. Hardy, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.1665 71, 1665 (1993).
15. J. Conway and S. Kochen, Found. Phys. FNDPA4 0015-9018 10.1007/s10701-006-9068-6 36, 1441 (2006); (Pubitemid 44832720)
16. J. H. Conway and S. Kochen, Notices AMS 56, 226 (2009).
17. C. Branciard, Nat. Phys. FNDPA4 1745-2473 10.1038/nphys1020 4, 681 (2008).
18. M. J. W. Hall, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105. 250404 105, 250404 (2010).
19. M. J. W. Hall, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.82.062117 82, 062117 (2010).
20. J. P. Jarrett, Noûs 18, 569 (1984).
21. E. Schrödinger, Proc. Am. Philos. Soc. 124, 323 (1980).
22. N. Bohr, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.48.696 48, 696 (1935).
23. C. M. Caves, C. A. Fuchs, and R. Schack, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.022305 65, 022305 (2002).
24. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.47.777 47, 777 (1935).
25. H. Everett III, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.29. 454 29, 454 (1957).
26. 1 / 2)], where p ranges over all underlying marginal probabilities.
27. P. Rastall, Found. Phys. FNDPA4 0015-9018 10.1007/BF00739036 15, 963 (1985);
28. S. Popescu and D. Rohrlich, Found. Phys. FNDPA4 0015-9018 10.1007/BF02058098 24, 379 (1994).
29. The mutual information H (K: L) for two jointly measured random variables K and L quantifies the number of bits of information obtained per member of a sequence of values of K about the corresponding sequence of values of L, and vice versa.
30. A. A. Fedotov, P. Harremoës, and F. Topsoe, IEEE Trans. Inf. Theory IETTAW 0018-9448 10.1109/TIT.2003.811927 49, 1491 (2003).
31. D. Dürr, S. Goldstein, and N. Zanghi, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01049004 67, 843 (1992).
32. A. Valentini and H. Westman, Proc. R. Soc. London, Ser. A JSTPBS 1364-5021 10.1098/rspa.2004.1394 461, 253 (2005); (Pubitemid 40522480)
33. A. F. Bennett, J. Phys. A 1751-8113 10.1088/1751-8113/43/19/195304 43, 195304 (2010).
34. 2 → 1, by summations. This measure is the maximum possible variational distance between two marginal distributions due to signaling. For the case of two-valued outcomes, it is just twice the value of the measure S defined in Eq..
35. B. F. Toner and D. Bacon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.187904 91, 187904 (2003).
36. Note that relativistic versions of communication models require a covariant time ordering, to specify the first observer. This can be defined, for example, via a preferred reference frame, or by the order in which the successive backward (or forward) light cones of a preferred clock trajectory intersect events in space-time.
37. 1), but oscillates between 1/3 and 2/3. Hence, the alternative forms of measurement independence given following Eq. are not always well defined, making Eq. the preferred form. Similarly, some measures of the degree of measurement dependence, such as mutual information, require p (x, y) to be well defined, and so can not be universally applied.
38. C. Brans, Int. J. Theor. Phys. 0020-7748 10.1007/BF00670750 27, 219 (1988).
39. H. Price, Mind IJTPBM 0026-4423 10.1093/mind/103.411.303 103, 411 (1994);
40. H. Price, Stud. Hist. Philos. Mod. Phys. IJTPBM 1355-2198 10.1016/j.shpsb.2008.05.006 35, 752 (2008).
41. J. Barrett and N. Gisin, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett. 106.100406 106, 100406 (2011).
42. G. Kar, J. Phys. A: Math. Theor. 1751-8113 10.1088/1751-8113/44/15/152002 44, 152002 (2011).
43. ′ X, Y) = H (M, Λ | X, Y).
44. A. Fine, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.48.291 48, 291 (1982).
45. M. Pawlowski, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/12/8/083051 12, 083051 (2010).
46. A. Peres, J. Phys. A: Math. Theor. JPHAC5 0305-4470 10.1088/0305-4470/24/ 4/003 24, L175 (1991).
47. J. Degorre, S. Laplante, and J. Roland, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.062314 72, 062314 (2005). (Pubitemid 43272674)
48. M. J. W. Hall, Int. J. Theor. Phys. IJTPBM 0020-7748 10.1007/BF00671311 27, 1285 (1988)
49. A. Fine, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.525514 23, 1306 (1982).
50. ′) depend on the entirety of the particular set of measurement pairs under consideration, the model is nonlocally contextual.