Quantum Experimental Proof

Wen-Rong Qi, Jie Zhou, Ling‐Jun Kong +9 more

A Hardy-like proof of quantum contextuality is a compelling way to see the conflict between quantum theory and noncontextual hidden variables (NCHVs), as the latter predict that a particular probability must be zero, while quantum theory predicts a nonzero value. For the existing Hardy-like proofs, the success probability tends to 1/2 when the number of measurement settings n goes to infinity. It means the conflict between the existing Hardy-like proof and NCHV theory is weak, which is not conducive to experimental observation. Here we advance the study of a stronger Hardy-like proof of quantum contextuality, whose success probability is always higher than the previous ones generated from a certain n -cycle graph. Furthermore, the success probability tends to 1 when n goes to infinity. We perform the experimental test of the Hardy-like proof in the simplest case of n = 7 by using a four-dimensional quantum system encoded in the polarization and orbital angular momentum of single photons. The experimental result agrees with the theoretical prediction within experimental errors. In addition, by starting from our Hardy-like proof, one can establish the stronger noncontextuality inequality, for which the quantum-classical ratio is higher with the same n , which provides a new method to construct some optimal noncontextuality inequalities. Our results offer a way for optimizing and enriching exclusivity graphs, helping to explore more abundant quantum properties.

Ian B. Spielman

F. Romanelli

W. vanDam, Richard David Gill, Peter Grünwald

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

Dominique Unruh

V. A. Kuz’menko

A number of direct and indirect experimental proofs of nonequivalence of forward and reversed processes in quantum physics are discussed. Their strong inequality is a real physical base of nonlinear optics.