Volume 8, Issue 2, pages 117-124
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 (MI) 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 MI without evoking super-determinism. They assume the independence of the variables that causally determine the settings and investigate how they might become correlated with hidden variables (e.g., when the cosmic photons enter the laboratory). 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 non-signaling 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 MI 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.