Coincidence Bell inequality for three three-dimensional systems

Abstract

A Bell inequality for coincidence probabilities on a three-dimensional (qutrit) system was constructed. The inequality was shown to be violated when each observer measures two noncommuting observables, defined by the six-port beam splitter on a maximally entangled states of two qutrits. For two particles of dimension greater than two, it was observed that the CHSH inequality can be violated in higher dimension system. It was also proven that the inequality defines facets of the polytope of local variable models.