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GHZ States as Tripartite PR Boxes: Classical Limit and Retrocausality.
Daniel Rohrlich1, Guy Hetzroni2
1Department of Physics, Ben-Gurion University of the Negev, Beersheba 84105, Israel.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
The argument that PR-box correlations violate relativistic causality in the classical limit does not extend to Greenberger-Horne-Zeilinger (GHZ) correlations. While both can be retrocausal, only GHZ correlations avoid self-contradictory causal loops.
Area of Science:
- Quantum Information Theory
- Foundations of Physics
Background:
- Bipartite "PR-box" correlations are theoretical constructs designed to respect relativistic causality.
- An argument suggests these PR-box correlations actually violate relativistic causality in the classical limit.
Purpose of the Study:
- To test the validity of the argument concerning PR-box correlations by examining its extension to tripartite Greenberger-Horne-Zeilinger (GHZ) correlations.
- To investigate the retrocausal properties of both PR-box and GHZ correlations and their implications for causal loops.
Main Methods:
- Reviewing the argument about PR-box correlations and relativistic causality.
- Analyzing Greenberger-Horne-Zeilinger (GHZ) correlations as a tripartite analogue of PR-box correlations.
- Evaluating the retrocausal nature of both correlation types and their consistency with causal principles.
Main Results:
- The argument that PR-box correlations violate relativistic causality in the classical limit does not extend to GHZ correlations.
- GHZ correlations respect relativistic causality in the classical limit, indicating a flaw in the original argument.
- Both PR-box and GHZ correlations can exhibit retrocausality, but GHZ correlations do not lead to self-contradictory causal loops.
Conclusions:
- The initial argument regarding PR-box correlations and relativistic causality is not universally applicable.
- GHZ correlations offer a consistent framework for exploring retrocausality without violating causal principles.
- This research clarifies the nuanced relationship between quantum correlations, causality, and retrocausality in theoretical physics.
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