Clauser-Horne inequality for three-state systems

Abstract

36 (of which 32 are independent) inequalities were derived as a necessary condition for the probabilities of correlations observed in two three-dimensional physical systems to be describable in terms of local realism. It was shown that these inequalities are violated by maximally entangled state of two qutrits and the strength of violation defined as the minimal noise admixture Fthr hiding nonclassical nature of quantum correlations agrees with the numerical results in previous studies. Using the inequalities, the critical quantum efficiency of detectors ηcr below which there exists a local realistic description of the investigated quantum system was calculated. The results are consistent with the hypothesis that the inequalities are also sufficient conditions for local realistic description.