Operational approach to Bell inequalities: applications to qutrits

TL;DR

This paper explores an operational approach to Bell inequalities using multipartite operators, discovering new inequalities for qutrits with multiple parties and proposing a novel generation method based on entangled states.

Contribution

It introduces a new operational framework for Bell inequalities, deriving novel inequalities for qutrits with multiple parties and a method to generate them from entangled states.

Findings

New Bell inequalities for three-outcome systems with 3 to 6 parties

Classical bounds and maximum quantum violations for these inequalities

A novel method to generate Bell inequalities from maximally entangled states

Abstract

Bell inequalities can be studied both as constraints in the space of probability distributions and as expectation values of multipartite operators. The latter approach is particularly useful when considering outcomes as eigenvalues of unitary operators. This brings the possibility of exploiting the complex structure of the coefficients in the Bell operators. We investigate this avenue of though in the known case of two outcomes, and find new Bell inequalities for the cases of three outcomes and $n=3,4,5$ and $6$ parties. We find their corresponding classical bounds and their maximum violation in the case of qutrits. We further propose a novel way to generate Bell inequalities based on a mapping from maximally entangled states to Bell operators and produce examples for different outcomes and number of parties.