Quantifying Bell non-locality with the trace distance

TL;DR

This paper introduces a new method to quantify quantum non-locality using trace distance, which is computationally efficient and applicable to various Bell scenarios, enhancing understanding and measurement of quantum correlations.

Contribution

It proposes a trace distance-based measure of non-locality that is a monotone under resource operations and can be efficiently computed via linear programming.

Findings

The trace distance measure is a valid non-locality quantifier.

It can be computed efficiently with linear programming.

The measure compares favorably with existing non-locality measures.

Abstract

Measurements performed on distant parts of an entangled quantum state can generate correlations incompatible with classical theories respecting the assumption of local causality. This is the phenomenon known as quantum non-locality that, apart from its fundamental role, can also be put to practical use in applications such as cryptography and distributed computing. Clearly, developing ways of quantifying non-locality is an important primitive in this scenario. Here, we propose to quantify the non-locality of a given probability distribution via its trace distance to the set of classical correlations. We show that this measure is a monotone under the free operations of a resource theory and that furthermore can be computed efficiently with a linear program. We put our framework to use in a variety of relevant Bell scenarios also comparing the trace distance to other standard measures in the literature.