GHZ States as Tripartite PR Boxes: Classical Limit and Retrocausality

Abstract

We review an argument that bipartite "PR-box" correlations, though designed to respect relativistic causality, in fact violate relativistic causality in the classical limit. As a test of this argument, we consider Greenberger-Horne-Zeilinger (GHZ) correlations as a tripartite version of PR-box correlations, and ask whether the argument extends to GHZ correlations. If it does-i.e., if it shows that GHZ correlations violate relativistic causality in the classical limit-then the argument must be incorrect (since GHZ correlations do respect relativistic causality in the classical limit.) However, we find that the argument does not extend to GHZ correlations. 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.

Quantum Nonlocality

“…The main test bed for considering nonlocal theories has been the example of PR boxes. It is the topic of the contribution by Rohrlich and Hetzroni [ 14 ], “GHZ States as Tripartite PR Boxes: Classical Limit and Retrocausality”. The starting point of this work is Rohrlich’s questioning of his own discovery: can we obtain a classical limit for PR boxes [ 15 ]?…”