Finding optimal Bell inequalities using the cone-projection technique

TL;DR

This paper extends the cone-projection technique to find and analyze new optimal Bell inequalities for multiple particles, enhancing computational methods in quantum information science.

Contribution

It generalizes existing Bell inequalities to more particles and introduces new inequalities using the cone-projection method, broadening the scope of quantum nonlocality tests.

Findings

Generalized I4422 inequality to three particles

Extended GYNI inequality to four particles

Identified Bell inequalities that unify I3322 and CHSH inequalities

Abstract

Bell inequalities are relevant for many problems in quantum information science, but finding them for many particles is computationally hard. Recently, a computationally feasible method called cone-projection technique has been developed to find all optimal Bell inequalities under some constraints, which may be given by some symmetry or other linear conditions. In this paper we extend this work in several directions. We use the method to generalize the I4422 inequality to three particles and a so-called GYNI inequality to four particles. Additionally, we find Bell inequalities for three particles that generalize the I3322 inequality and the CHSH inequality at the same time. We discuss the obtained inequalities in some detail and characterize their violation in quantum mechanics.