Finite Statistics Loophole in CH, Eberhard, CHSH Inequalities
Justin Lee
Clauser-Horne (CH) inequality, Eberhard inequality, and Clauser-Horne-Shimony-Holt (CHSH) inequality are used to determine whether quantum entanglement can contradict local realism. However, the loophole is known to allow local realism to violate these inequalities if a sample size is small and not enough [1]. Remarkably though, this paper shows that this loophole can still cause a violation in these inequalities even with a very large sample size, e.g. a 2.4 sigma violation of CH inequality and Eberhard inequality was achieved despite 12,000,000 total trials in a Monte Carlo simulation of a local realist photonic experiment based on Malus' law. In addition, this paper shows how Eberhard inequality is especially vulnerable to this loophole when combined with an improper statistical analysis and incorrect singles counts, e.g. a 13.0 sigma violation was achieved with the same large sample size, and furthermore, a 26.6 sigma violation was produced when a small, acceptable 0.2% production rate loophole was applied. Supplementally, this paper demonstrates how the finite statistics loophole allows a bigger violation in a smaller sample size despite the sample size being enough, e.g. a CHSH violation of 4.4 sigma (2.43 +/- 0.10) was achieved with 280 total trials, and 4.0 sigma (2.16 +/- 0.04) with 3,000 total trials. This paper introduces the aforementioned loopholes as plausible local realist explanations to two observed violations reported by Giustina, et al. [2], and Hensen, et al. [3].
•Mar 1, 2018•0 citations