Contextuality-by-Default description of Bell tests: Contextuality as the rule not as an exception

TL;DR

This paper applies the Contextuality-by-Default framework to Bell tests, demonstrating that contextuality is fundamental and should be systematically examined in quantum experiments, challenging traditional assumptions about non-contextuality.

Contribution

It introduces a novel analysis of Bell tests using the Contextuality-by-Default approach, accounting for inconsistent connectedness and setting-dependent variables.

Findings

Bell inequality violations explained by contextual models

Inconsistent connectedness is inherent in Bell test data

Contextuality appears as a fundamental rule in quantum measurements

Abstract

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 behavioral 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 and Bob raw data confirm Einsteinian non-signaling, but setting dependent experimental protocols are used to create samples of coupled pairs of distant 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.