The statistical strength of nonlocality proofs

The strength of a nonlocality proof is examined in terms of the amount of evidence that the corresponding experiment provides for the nonlocality of Nature. An experimental implementation of such a proof gives data whose statistics will differ from the statistics that are possible under a local description of Nature. The strength of the experiment is quantified by the expected deviation between the observed frequencies, which are given by the laws of quantum mechanics, and the closest possible local theory. Varying the frequencies of the measurement settings gives different experimental implementations of a nonlocality proof, giving each implementation its own strength. The statistical strength of a nonlocality proof is thus determined by the experimental implementation that maximizes its statistical deviation from all possible local theories. It is shown that the deviation between quantum mechanics and a local theory is best expressed by the Kullback-Leibler distance between the probability distributions over the measurement outcomes that the respective theories predict. Specifically, it is proven that the Kullback-Leibler distance is optimal for three methods of hypothesis testing: frequentist, Bayesian, and information theoretic hypothesis testing. The nonlocality proofs that are analyzed in this article are: Bell’s original proof, an improved version