Characterization of non-signaling correlations from mutual information

TL;DR

This paper introduces a new two-dimensional representation of non-signaling correlations using Bell functional values and mutual information, providing insights into quantum and post-quantum boundaries without relying on quantum mechanics.

Contribution

It offers a novel characterization of non-signaling correlations through a physically meaningful two-dimensional framework, combining numerical and analytical methods.

Findings

Tsirelson bound appears as a singular point in the correlation landscape

The representation distinguishes quantum from post-quantum correlations

Numerical optimization clarifies the boundary between different correlation sets

Abstract

We present a characterization of the set of non-signaling correlations in terms of a two dimensional representation that involves the maximal value of a Bell functional and the mutual information between the parties. In particular, we apply this representation to the bipartite Bell scenario with two measurements and two outcomes. In terms of these physically meaningful quantities and through numerical optimization methods and some analytical results, we investigate the frontier between the different subsets of the non-signaling correlations, focussing on the quantum and post-quantum ones. Finally, we show that the Tsirelson bound appears as a singular point in this context without resorting to quantum mechanics.