Two-Party Bell Inequalities Derived from Combinatorics via Triangular Elimination

Details Two-Party Bell Inequalities Derived from Combinatorics via Triangular Elimination Two-Party Bell Inequalities Derived from Combinatorics via Triangular Elimination

2005-05-09

arxiv.org/abs/quant-ph/0505060v3

Physics

Quantum Physics

Part of results in Section 2 appeared in quant-ph/0404014, but this paper gives new proofs using only elementary mathematics.

Scientific paper

We establish a relation between the two-party Bell inequalities for two-valued measurements and a high-dimensional convex polytope called the cut polytope in polyhedral combinatorics. Using this relation, we propose a method, triangular elimination, to derive tight Bell inequalities from facets of the cut polytope. This method gives two hundred million inequivalent tight Bell inequalities from currently known results on the cut polytope. In addition, this method gives general formulas which represent families of infinitely many Bell inequalities. These results can be used to examine general properties of Bell inequalities.

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