A unifying framework for relaxations of the causal assumptions in Bell's theorem

TL;DR

This paper introduces a unified, computationally tractable framework using Bayesian networks to analyze how relaxing causal assumptions like locality and measurement independence can explain quantum correlations violating Bell's theorem.

Contribution

It develops a systematic, quantitative approach to relax causal assumptions in Bell's theorem using Bayesian networks and linear programming, enabling new insights into classical explanations of quantum correlations.

Findings

Framework applies to various causal assumption relaxations.

Linear programs efficiently bound degrees of assumption relaxation.

Provides a new causal interpretation of CHSH inequality violations.

Abstract

Bell's Theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions -- e.g. locality or measurement independence -- have to be relaxed in order to allow for a classical description of such experiments. Here, we develop a conceptual and computational framework for treating this problem. We employ the language of Bayesian networks to systematically construct alternative causal structures and bound the degree of relaxation using quantitative measures that originate from the mathematical theory of causality. The main technical insight is that the resulting problems can often be expressed as computationally tractable linear programs. We demonstrate the versatility of the framework by applying it to a variety of scenarios, ranging from relaxations of the measurement independence, locality and bilocality assumptions, to a novel causal interpretation of CHSH inequality violations.