GHZ states and PR boxes in the classical limit

TL;DR

This paper tests whether GHZ correlations, as a tripartite extension of PR-box correlations, violate relativistic causality in the classical limit, and finds that they do not, challenging previous claims about PR-boxes.

Contribution

The paper demonstrates that GHZ correlations do not violate relativistic causality in the classical limit, unlike PR-box correlations, and clarifies the nature of retrocausality in these correlations.

Findings

GHZ correlations do not violate relativistic causality in the classical limit.

PR-box correlations lead to self-contradictory causal loops when retrocausal.

GHZ correlations can be retrocausal without contradictions.

Abstract

A recent paper [1] argues that bipartite "PR-box" correlations, though designed to respect relativistic causality, in fact violate relativistic causality in the classical limit. As a test of Ref. [1], we consider GHZ correlations as a tripartite version of PR-box correlations, and ask whether the arguments of Ref. [1] extend to GHZ correlations. If they do - i.e. if they show that GHZ correlations violate relativistic causality in the classical limit - then Ref. [1] must be incorrect, since GHZ correlations are quantum correlations and respect relativistic causality. But the arguments fail. We also show that both PR-box correlations and GHZ correlations can be retrocausal, but the retrocausality of PR-box correlations leads to self-contradictory causal loops, while the retrocausality of GHZ correlations does not.