A complete set of multidimensional Bell inequalities

Abstract

We give a multidimensional generalisation of the complete set of\nBell-correlation inequalities given by Werner and Wolf, and by Zukowski and\nBrukner, for the two-dimensional case. Our construction applies for the n\nparties, two-observables case, where each observable is d-valued. The d^{d^n}\ninequalities obtained involve homogeneous polynomials. They define the facets\nof a polytope in a complex vector space of dimension d^n. We also show that\nthese inequalities are violated by Quantum Mechanics. We exhibit examples in\nthe three-dimensional case.\n