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Examples and Counterexamples

On a conjecture of Gill on Bell experiments

Daniel B. Rubin

Published Oct 10, 2025• 0 citations
Publisher

Abstract

This note gives a counterexample to a conjecture of Richard Gill that was stated as open problem related to the statistical analysis of Bell experiments in quantum mechanics, and which can formulated as an elementary probability problem.
DOI
10.1016/j.exco.2025.100203

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The aim of this note is to attract once again attention of the quantum community to statistical analysis of data which was reported as violating Bell's inequality. This analysis suffers of a number of problems. And the main problem is that rough data is practically unavailable. However, experiments which are not followed by the open access to the rough data have to be considered as with no result. The absence of rough data generates a variety of problems in statistical interpretation of the results of Bell's type experiment. One may hope that this note would stimulate experimenters to create the open access data-base for, e.g., Bell tests. Unfortunately, recently announced experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km was not supported by open-access data. Therefore in accordance with our approach "it has no result." The promising data after publication is, of course, a step towards fair analysis quantum experiments. May be this is a consequence of appearance of this preprint, v1. But there are a few questions which would be interesting to clarify before publication (and which we shall discuss in this note).