A complete set of multidimensional Bell inequalities

作者:Arnault Francois*
来源:Journal of Physics A-Mathematical and Theoretical, 2012, 45(25): 255304.
DOI:10.1088/1751-8113/45/25/255304

摘要

We give a multidimensional generalization of the complete set of Bell-correlation inequalities given by Werner and Wolf (2001 Phys. Rev. A 64 032112) and by Zukowski and Brukner (2002 Phys. Rev. Lett. 88 210401), for the two-dimensional case. Our construction applies to the n-party, two-observable case, where each observable is d-valued. The d(dn) inequalities obtained involve homogeneous polynomials. They define the facets of a polytope in a complex vector space of dimension d(n). We detail the inequalities obtained in the case d = 3 and, from them, we recover known inequalities. We finally explain how the violations of our inequalities by quantum mechanics can be computed and could be observed, when using unitary observables.

  • 出版日期2012-6-29