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Exploring inequality violations by classical hidden variables numerically. (English) Zbl 1343.81010
Summary: There are increasingly suggestions for computer simulations of quantum statistics which try to violate Bell type inequalities via classical, common cause correlations. The Clauser-Horne-Shimony-Holt (CHSH) inequality is very robust. However, we argue that with the Einstein-Podolsky-Rosen setup, the CHSH is inferior to the Bell inequality, although and because the latter must assume anti-correlation of entangled photon singlet states. We simulate how often quantum behavior violates both inequalities, depending on the number of photons. Violating Bell 99% of the time is argued to be an ideal benchmark. We present hidden variables that violate the Bell and CHSH inequalities with 50% probability, and ones which violate Bell 85% of the time when missing 13% anti-correlation. We discuss how to present the quantum correlations to a wide audience and conclude that, when defending against claims of hidden classicality, one should demand numerical simulations and insist on anti-correlation and the full amount of Bell violation.

MSC:
81P05 General and philosophical questions in quantum theory
81S05 Commutation relations and statistics as related to quantum mechanics (general)
81P40 Quantum coherence, entanglement, quantum correlations
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[1] Ekert, A. K., Phys. Rev., 67, 661, (1991)
[2] Aspect, A.; Grangier, P.; Roger, G., Phys. Rev. Lett., 47, 460-463, (1981)
[3] Aspect, A.; Grangier, P.; Roger, G., Phys. Rev. Lett., 48, 91-94, (1982)
[4] Einstein, A.; Podolsky, B.; Rosen, N., Phys. Rev., 47, 10, 777-780, (1935)
[5] Bell, J. S., Physics, 1, 3, 195-200, (1964)
[6] Bell, J. S., Rev. Modern Phys., 38, 447-452, (1966)
[7] Clauser, J. F.; Horne, M. A.; Shimony, A.; Holt, R. A., Phys. Rev. Lett., 23, 880-884, (1969)
[8] Weihs, G.; Jennewein, T.; Simon, C.; Weinfurter, H.; Zeilinger, A., Phys. Rev. Lett., 81, 5039-5043, (1998)
[9] Barrett, J.; Hardy, L.; Kent, A., Phys. Rev. Lett., 95, 010503, (2005)
[10] Acin, A.; Gisin, N.; Masanes, L., Phys. Rev. Lett., 97, 120405, (2006)
[11] Gill, R. D., (Proc of Foundation of Probability and Physics—Vol. 2, (2002), Ser. Math. Modelling in Phys., Engin. and Cogn. Sci., vol. 5, (2003), Vaxjo Univ. Press), 179-206
[12] Aspect, A., Nature, 394, 18, 189-190, (1999)
[13] Vaidman, L., Phys. Lett. A, 286, 241-244, (2001)
[14] Gill, R. D.; Larsson, J. A., (Moore, M.; Froda, S.; L’eger, C., Mathematical Statistics and Applications: Festschrift for Constance van Eeden, Monograph Series, vol. 42, (2003), Institute of Mathematical Statistics Beachwood, Ohio), 133-154
[15] S. Vongehr, 2012. arxiv.org/abs/1207.5294v3.
[16] Peres, A., Amer. J. Phys., 46, 7, 745-747, (1978)
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