Deriving three-outcome permutationally invariant Bell inequalities

TL;DR

This paper develops methods to derive Bell inequalities for multipartite three-level systems, enabling detection of nonlocality with complexity independent of the number of parties, applicable to spin-1 models and solid-state experiments.

Contribution

The authors introduce two new methods for deriving Bell inequalities in multipartite three-level systems that are computationally scalable and applicable to various physical platforms.

Findings

Derived Bell inequalities for systems with many three-level parties.

Methods are independent of the number of parties, N.

Applicable to spin-1 models and solid-state experiments.

Abstract

We present strategies to derive Bell inequalities valid for systems composed of many three-level parties. This scenario is formalized by a Bell experiment with $N$ observers, each of which performs one out of two possible three-outcome measurements on their share of the system. As the complexity of the set of classical correlations prohibits its full characterization in this multipartite scenario, we consider its projection to a lower dimensional subspace spanned by permutationally invariant one- and two-body observables. This simplification allows us to formulate two complementary methods for detecting nonlocality in multipartite three-level systems, both having a complexity independent of $N$. Our work can have interesting applications in the detection of Bell correlations in paradigmatic spin-1 models, as well as in experiments with solid-state systems or atomic ensembles.