GHZ states as tripartite PR boxes: Classical limit and retrocausality

Daniel Rohrlich, Guy Hetzroni

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number478
Issue number6
StatePublished - 1 Jun 2018
Externally publishedYes

Bibliographical note

Funding Information:
Acknowledgments: We thank all the Referees for helpful comments. This publication was made possible through the support of grants from the John Templeton Foundation (Project ID 43297), from the Israel Science Foundation (grant no. 1190/13). The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of either of these supporting foundations.

Publisher Copyright:
© 2019 by the authors.


  • Axioms for quantum theory
  • Classical limit
  • Nonlocal correlations
  • PR box
  • Retrocausality


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