Comment on Causal Networks and Freedom of Choice in Bell's Theorem

TL;DR

This paper critiques the concept of freedom of choice in Bell's theorem, arguing that contextuality, not free will, explains quantum correlations and violations of Bell inequalities within a locally causal framework.

Contribution

It demonstrates that violations of measurement independence can be explained through contextual probabilistic models without invoking super-determinism or compromising experimenters' free will.

Findings

Contextual probabilistic models explain Bell test violations locally.

Freedom of choice is better understood as noncontextuality.

Bell inequalities do not necessarily imply nonlocality.

Abstract

Bell inequalities may only be derived, if hidden variables do not depend on the experimental settings. The stochastic independence of hidden and setting variables is called: freedom of choice, free will, measurement independence or no conspiracy. By imbedding the Bell causal structure in a larger causal network the authors correctly prove, that one can explain and quantify possible violation of measurement independence without evoking the super-determinism. They assume the independence of the variables that causally determine the settings and investigate how they might become correlated with hidden variables. Using their extended causal networks they derive a contextual probabilistic model on which their further correct results are based. The authors seem to ignore that contextual probabilistic model may be derived directly using only probabilistic concepts and incorporating correctly setting dependent variables describing measuring instruments. In these contextual probabilistic models experimenters freedom of choice is not compromised and the results of Bell Tests including an apparent violation of Einsteinian nonsignaling may be explained in a locally causal way. Talking about freedom of choice is misleading and is rooted in incorrect understanding of Bayes Theorem. We explain why freedom of choice should be called noncontextuality and why its violation in Bell Tests confirms only the contextual character of quantum observables. Therefore, contextuality and not experimenters freedom of choice are important resources in quantum information.