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Violations of locality and free choice are equivalent resources in Bell experiments

Blasiak, P., Pothos, E. M. ORCID: 0000-0003-1919-387X, Yearsley, J. ORCID: 0000-0003-4604-1839 , Gallus, C. & Borsuk, E. (2021). Violations of locality and free choice are equivalent resources in Bell experiments. Proceedings of the National Academy of Sciences of USA, 118(17), article number e202056911. doi: 10.1073/pnas.2020569118


Bell inequalities rest on three fundamental assumptions: realism, locality, and free choice, which lead to nontrivial constraints on correlations in very simple experiments. If we retain realism, then violation of the inequalities implies that at least one of the remaining two assumptions must fail, which can have profound consequences for the causal explanation of the experiment. We investigate the extent to which a given assumption needs to be relaxed for the other to hold at all costs, based on the observation that a violation need not occur on every experimental trial, even when describing correlations violating Bell inequalities. How often this needs to be the case determines the degree of, respectively, locality or free choice in the observed experimental behavior. Despite their disparate character, we show that both assumptions are equally costly. Namely, the resources required to explain the experimental statistics (measured by the frequency of causal interventions of either sort) are exactly the same. Furthermore, we compute such defined measures of locality and free choice for any nonsignaling statistics in a Bell experiment with binary settings, showing that it is directly related to the amount of violation of the so-called Clauser–Horne–Shimony–Holt inequalities. This result is theory independent as it refers directly to the experimental statistics. Additionally, we show how the local fraction results for quantum-mechanical frameworks with infinite number of settings translate into analogous statements for the measure of free choice we introduce. Thus, concerning statistics, causal explanations resorting to either locality or free choice violations are fully interchangeable.

Publication Type: Article
Publisher Keywords: locality, free choice, causal models, non-local correlations, Bell inequalities, measure of locality, measure of free choice
Subjects: B Philosophy. Psychology. Religion > BF Psychology
Departments: School of Health & Psychological Sciences > Psychology
SWORD Depositor:
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