zbMATH — the first resource for mathematics

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.

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
Full Text: DOI
[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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.