The CHSH Game, Tsirelson's Bound, and Causal Locality

TL;DR

This paper introduces a new proof of Tsirelson's bound by reformulating the CHSH game through indivisible stochastic processes and causal locality, highlighting the role of causally local processes in quantum correlations.

Contribution

It presents a novel proof of Tsirelson's bound using a reformulation of the CHSH game with indivisible stochastic processes and causal locality principles.

Findings

Causally local, indivisible stochastic processes can violate Bell inequalities up to Tsirelson's bound.

The proof connects causal locality with quantum correlations and Tsirelson's limit.

Reformulation offers new insights into the foundations of quantum nonlocality.

Abstract

We reformulate the CHSH game in terms of indivisible stochastic processes. Using Barandes's stochastic-quantum correspondence and its associated definition of causal locality, we present a novel proof of the Tsirelson bound. In particular, we show that unlike the no-signaling principle alone, the postulates defining causally local, indivisible stochastic processes are precisely strong enough to allow for violations of the Bell inequality up to, but not beyond, the Tsirelson bound.