A game-theoretic probability approach to loopholes in CHSH experiments

TL;DR

This paper applies a game-theoretic probability framework to analyze CHSH experiments, reformulating loopholes as structural constraints and demonstrating that Nature cannot satisfy all conditions simultaneously, providing a new interpretation of CHSH violations.

Contribution

It introduces a game-theoretic approach to analyze CHSH loopholes, offering a novel perspective that does not rely on traditional probability models.

Findings

Nature cannot satisfy all loophole constraints simultaneously

Constructed a loopholes-closed game with testable capital processes

Provided a game-theoretic interpretation of CHSH violations

Abstract

We study the CHSH inequality from an informational, timing-sensitive viewpoint using game-theoretic probability, which avoids assuming an underlying probability space. The locality loophole and the measurement-dependence (``freedom-of-choice'') loophole are reformulated as structural constraints in a sequential hidden-variable game between Scientists and Nature. We construct a loopholes-closed game with capital processes that test (i) convergence of empirical conditional frequencies to the CHSH correlations and (ii) the absence of systematic correlations between measurement settings and Nature's hidden-variable assignments, and prove that Nature cannot satisfy both simultaneously: at least one capital process must diverge. This yields an operational winning strategy for Scientists and a game-theoretic probabilistic interpretation of experimentally observed CHSH violations.