Nonlocality is transitive

TL;DR

This paper demonstrates a transitivity property of nonlocal correlations in tripartite systems, showing that pairwise nonlocality implies the nonlocality of the third pair, which challenges certain hidden communication models of quantum correlations.

Contribution

It introduces a transitivity property of nonlocal correlations in tripartite systems, advancing understanding of quantum nonlocality and its implications for hidden communication models.

Findings

Existence of tripartite correlations with pairwise nonlocal marginals

Tripartite nonlocality is transitive among the parties

Implications for ruling out finite-speed hidden communication models

Abstract

We show a transitivity property of nonlocal correlations: There exist tripartite nonsignaling correlations of which the bipartite marginals between A and B as well as B and C are nonlocal and any tripartite nonsignaling system between A, B, and C consistent with them must be such that the bipartite marginal between A and C is also nonlocal. This property represents a step towards ruling out certain alternative models for the explanation of quantum correlations such as hidden communication at finite speed. Whereas it is not possible to rule out this model experimentally, it is the goal of our approach to demonstrate this explanation to be logically inconsistent: either the communication cannot remain hidden, or its speed has to be infinite. The existence of a three-party system that is pairwise nonlocal is of independent interest in the light of the monogamy property of nonlocality.