Coincidence Bell Inequality for Three Three-Dimensional Systems

We construct a Bell inequality for coincidence probabilities on a three three-dimensional (qutrit) system. We show that this inequality is violated when each observer measures two noncommuting observables, defined by the so-called unbiased six-port beam splitter, on a maximally entangled state of two qutrits. The strength of the violation agrees with the numerical results presented by Kaszlikowski et al, quant-ph/0202019. It is proven that the inequality defines facets of the polytope of local variable models.