PR-box correlations have no classical limit

TL;DR

This paper demonstrates that PR-box correlations, which are superquantum, violate relativistic causality in the classical limit, providing a derivation of Tsirelson's bound without assuming quantum mechanics.

Contribution

It introduces a minimal third axiom about the classical limit and shows that PR-box correlations violate causality in this limit, deriving Tsirelson's bound independently of quantum mechanics.

Findings

PR-box correlations violate relativistic causality in the classical limit

Derivation of Tsirelson's bound without assuming quantum mechanics

Superquantum correlations cannot have a classical limit consistent with causality

Abstract

One of Yakir Aharonov's endlessly captivating physics ideas is the conjecture that two axioms, namely relativistic causality ("no superluminal signalling") and nonlocality, so nearly contradict each other that a unique theory - quantum mechanics - reconciles them. But superquantum (or "PR-box") correlations imply that quantum mechanics is not the most nonlocal theory (in the sense of nonlocal correlations) consistent with relativistic causality. Let us consider supplementing these two axioms with a minimal third axiom: there exists a classical limit in which macroscopic observables commute. That is, just as quantum mechanics has a classical limit, so must any generalization of quantum mechanics. In this classical limit, PR-box correlations violate relativistic causality. Generalized to all stronger-than-quantum bipartite correlations, this result is a derivation of Tsirelson's bound without assuming quantum mechanics.