A complete set of multidimensional Bell inequalities
Quantum Physics
2015-05-28 v2 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1107.2255,
title = {A complete set of multidimensional Bell inequalities},
author = {François Arnault},
journal= {arXiv preprint arXiv:1107.2255},
year = {2015}
}
Comments
14 pages, 1 figure. Plain TeX file This version 2 adds Section 7 about violations. Section 8 (the case d=3) and bibliography have been extended accordingly