Characterization of nonsignaling correlations from mutual information

We present a characterization of the set of nonsignaling 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 nonsignaling correlations, focusing on the quantum and postquantum ones. Our analysis exhibits that there is a trade-off between the amount of classical correlations existing between the parties and the magnitude of the violation of a given Bell inequality. Notably, the Tsirelson bound appears as a singular point of this trade-off without resorting to quantum mechanics.

Automated summary

The study characterizes the set of nonsignaling correlations using a two-dimensional representation involving the maximal value of a Bell functional and the mutual information between the parties. By investigating the frontier between quantum and postquantum subsets of nonsignaling correlations, the analysis reveals a trade-off between classical correlations and violations of Bell inequalities. The Tsirelson bound is identified as a singular point of this trade-off, independent of quantum mechanics.