Violations of local realism with quNits up to N=16

Abstract

Predictions for systems in entangled states cannot be described in local realistic terms. However, after admixing some noise such a description is possible. We show that for two quNits (quantum systems described by N dimensional Hilbert spaces) in a maximally entangled state the minimal admixture of noise increases monotonically with N. The results are a direct extension of those of Kaszlikowski et. al., Phys. Rev. Lett. {\bf 85}, 4418 (2000), where results for $N\leq 9$ were presented. The extension up to N=16 is possible when one defines for each N a specially chosen set of observables. We also present results concerning the critical detectors efficiency beyond which a valid test of local realism for entangled quNits is possible.