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arXiv · 1107.2255

A complete set of multidimensional Bell inequalities

François Arnault
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Abstract

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

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François Arnault. 2011-07-12. A complete set of multidimensional Bell inequalities. https://doi.org/10.1088/1751-8113/45/25/255304

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