Nonlocality free wirings and the distinguishability between Bell boxes

TL;DR

This paper explores how prior classical communication affects the distinguishability of Bell correlations, revealing new insights into nonlocality measures and the geometry of nonlocal behaviors within resource theories.

Contribution

It demonstrates that prior communication enables wirings beyond local operations with shared randomness, impacting nonlocality quantification and operational distinguishability.

Findings

Prior communication enhances distinguishability of Bell correlations.

Introduces a universal definition of Bell nonlocality measures.

Identifies issues in the standard statistical strength of nonlocality proofs.

Abstract

Bell nonlocality can be formulated in terms of a resource theory with local-hidden variable models as resourceless objects. Two such theories are known, one built upon local operations assisted by shared randomness (LOSRs) and the other one allowing, in addition, for prior-to-input classical communication. We show that prior communication, although unable to create nonlocality, leads to wirings not only beyond LOSRs but also not contained in a much broader class of (nonlocality-generating) global wirings. Technically, this is shown by proving that it can improve the statistical distinguishability between Bell correlations optimised over all fixed measurement choices. This has implications in nonlocality quantification, and leads us to a natural universal definition of Bell nonlocality measures. To end up with, we also consider the statistical strength of nonlocality proofs. We point out some issues of its standard definition in the resource-theoretic operational framework, and suggest simple fixes for them. Our findings reveal non-trivial features of the geometry of the set of wirings and may have implications in the operational distinguishability of nonlocal behaviors.