Bell inequalities from variable elimination methods

Details Bell inequalities from variable elimination methods Bell inequalities from variable elimination methods

2011-12-26

arxiv.org/abs/1112.5876v1

Physics

Quantum Physics

Scientific paper

Tight Bell inequalities are facets of Pitowsky's correlation polytope and are usually obtained from its extreme points by solving the hull problem. Recently, Avis, Imai, Ito and Sasaki have proposed an alternative method, based on variable elimination, which overcomes some of the computational difficulties of the hull problem. However, this method can only be applied to the bipartite case. Here we present an algebraic derivation of the half-space representation for a family of convex polytopes, from which every correlation polytope can be obtained as a projection. As a result, variable elimination methods, e.g. the Fourier-Motzkin method, can be applied to obtain tight Bell inequalities in an n-party scenario. Similar ideas are shown to be applicable to a different kind of algebraic conditions. In particular, this analysis provides an explanation for the fact that only a finite number of families of Bell inequalities arise in scenarios where one experimenter can choose between an arbitrary number of measurements.

Affiliated with

Also associated with

No associations

Rating

Bell inequalities from variable elimination methods does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bell inequalities from variable elimination methods, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bell inequalities from variable elimination methods will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-253232