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.
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.
A violation of Bell-CHSH inequalities does not justify speculations about quantum non-locality, conspiracy and retro-causation. Such speculations are rooted in a belief that setting dependence of hidden variables in a probabilistic model (called a violation of measurement independence (MI)) would mean a violation of experimenters’ freedom of choice. This belief is unfounded because it is based on a questionable use of Bayes Theorem and on incorrect causal interpretation of conditional probabilities. In Bell-local realistic model, hidden variables describe only photonic beams created by a source, thus they cannot depend on randomly chosen experimental settings. However, if hidden variables describing measuring instruments are correctly incorporated into a contextual probabilistic model a violation of inequalities and an apparent violation of no-signaling reported in Bell tests can be explained without evoking quantum non-locality. Therefore, for us, a violation of Bell-CHSH inequalities proves only that hidden variables have to depend on settings confirming contextual character of quantum observables and an active role played by measuring instruments. Bell thought that he had to choose between non-locality and the violation of experimenters’ freedom of choice. From two bad choices he chose non-locality. Today he would probably choose the violation of MI understood as contextuality.
Bell's theorem is typically understood as the proof that quantum theory is incompatible with localhidden-variable models.More generally, we can see the violation of a Bell inequality as witnessing the impossibility of explaining quantum correlations with classical causal models.The violation of a Bell inequality, however, does not exclude classical models where some level of measurement dependence is allowed, that is, the choice made by observers can be correlated with the source generating the systems to be measured.Here, we show that the level of measurement dependence can be quantitatively upper bounded if we arrange the Bell test within a network.Furthermore, we also prove that these results can be adapted in order to derive nonlinear Bell inequalities for a large class of causal networks and to identify quantumly realizable correlations that violate them.
In his article in Science, Nicolas Gisin claimed that quantum correlations emerge from outside space–time. We explainthat they are due to space-time symmetries. This paper is a critical review of metaphysical conclusions found in many recent articles. It advocates the importance of contextuality, Einstein -causality and global symmetries. Bell tests allow only rejecting probabilistic coupling provided by a local hidden variable model, but they do not justify metaphysical speculations about quantum nonlocality and objects which know about each other’s state, even when separated by large distances. The violation of Bell inequalities in physics and in cognitive science can be explained using the notion of Bohr- contextuality. If contextual variables, describing varying experimental contexts, are correctly incorporated into a probabilistic model, then the Bell–CHSH inequalities cannot be proven and nonlocal correlations may be explained in an intuitive way. We also elucidate the meaning of statistical independence assumption incorrectly called free choice, measurement independence or no- conspiracy. Since correlation does not imply causation, the violation of statistical independence should be called contextuality; it does not restrict the experimenter’s freedom of choice. Therefore, contrary to what is believed, closing the freedom-of choice loophole does not close the contextuality loophole.
Contextuality and entanglement are valuable resources for quantum computing and quantum information. Bell inequalities are used to certify entanglement; thus, it is important to understand why and how they are violated. Quantum mechanics and behavioural sciences teach us that random variables 'measuring' the same content (the answer to the same Yes or No question) may vary, if 'measured' jointly with other random variables. Alice's and BoB's raw data confirm Einsteinian non-signaling, but setting dependent experimental protocols are used to create samples of coupled pairs of distant ±1 outcomes and to estimate correlations. Marginal expectations, estimated using these final samples, depend on distant settings. Therefore, a system of random variables 'measured' in Bell tests is inconsistently connected and it should be analyzed using a Contextuality-by-Default approach, what is done for the first time in this paper. The violation of Bell inequalities and inconsistent connectedness may be explained using a contextual locally causal probabilistic model in which setting dependent variables describing measuring instruments are correctly incorporated. We prove that this model does not restrict experimenters' freedom of choice which is a prerequisite of science. Contextuality seems to be the rule and not an exception; thus, it should be carefully tested.
In our contextual model, statistical independence is violated, thus it is not constrained by Bell Theorem. Individual outcomes are created locally in a deterministic way in a function of setting dependent variables describing measuring instruments and variables describing physical systems, at the moment of their interactions. These setting dependent variables may be correlated, but not necessarily due to spooky influences or superdeterminism. In several Bell Tests, two time series of distant clicks are converted into finite samples containing pairs of non zero outcomes. This data not only violates CHSH inequalities but also nonsignalling. Our model allows explaining both the raw and the final data in these experiments. Moreover, our model, does not compromise experimenters freedom of choice. The violation of nonsignaling is neither consistent with quantum description of an ideal EPRB experiment nor with standard local realistic and stochastic hidden variable models, thus the title of this article and its conclusion: Kupczynski escape route for local realism is not available are misleading.
Bell's inequality was originally derived under the assumption that experimenters are free to select detector settings independently of any local ``hidden variables'' that might affect the outcomes of measurements on entangled particles. This assumption has come to be known as ``measurement independence'' (also referred to as ``freedom of choice'' or ``settings independence''). For a two-setting, two-outcome Bell test, we derive modified Bell inequalities that relax measurement independence, for either or both observers, while remaining locally causal. We describe the loss of measurement independence for each observer using the parameters M1 and M2, as defined by Hall in 2010, and also by a more complete description that adds two new parameters, which we call $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{{M}_{1}}$ and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{{M}_{2}}$, deriving a modified Bell inequality for each description. These ``relaxed'' inequalities subsume those considered in previous work as special cases, and quantify how much the assumption of measurement independence needs to be relaxed in order for a locally causal model to produce a given violation of the standard Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality. We show that both relaxed Bell inequalities are tight bounds on the CHSH parameter by constructing locally causal models that saturate them. For any given Bell inequality violation, the new two-parameter and four-parameter models each require significantly less mutual information between the hidden variables and measurement settings than previous models. We conjecture that the new models, with optimal parameters, require the minimum possible mutual information for a given Bell violation. We further argue that, contrary to various claims in the literature, relaxing freedom of choice need not imply superdeterminism.