Looking for symmetric Bell inequalities

TL;DR

This paper introduces a method to efficiently find symmetric Bell inequalities by analyzing a simplified symmetrized polytope, leading to the discovery of thousands of new inequalities, including some not of known types.

Contribution

The authors develop a novel approach to identify symmetric Bell inequalities using a symmetrized polytope, significantly expanding the known set of inequalities.

Findings

Generated 238,885 new Bell inequalities.

Discovered 1,085 new Svetlichny inequalities.

Found facet inequalities beyond the Collins-Gisin-Linden-Massar-Popescu type.

Abstract

Finding all Bell inequalities for a given number of parties, measurement settings, and measurement outcomes is in general a computationally hard task. We show that all Bell inequalities which are symmetric under the exchange of parties can be found by examining a symmetrized polytope which is simpler than the full Bell polytope. As an illustration of our method, we generate 238885 new Bell inequalities and 1085 new Svetlichny inequalities. We find, in particular, facet inequalities for Bell experiments involving two parties and two measurement settings that are not of the Collins-Gisin-Linden-Massar-Popescu type.