Optimal Statistical Analyses of Bell Experiments

We show how both smaller and more reliable p-values can be computed in Bell-type experiments by using statistical deviations from no-signalling equalities to reduce statistical noise in the estimation of Bell’s S or Eberhard’s J. Further improvement was obtained by using the Wilks likelihood ratio t...

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Bibliographic Details
Published in:AppliedMath 2023-06, Vol.3 (2), p.446-460
Main Author: Gill, Richard D.
Format: Article
Language:English
Subjects:
Bell experiment
Bell-CHSH inequality
maximum likelihood estimation
quantum entanglement
testing statistical hypotheses
Wilks generalized likelihood ratio test
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Summary:We show how both smaller and more reliable p-values can be computed in Bell-type experiments by using statistical deviations from no-signalling equalities to reduce statistical noise in the estimation of Bell’s S or Eberhard’s J. Further improvement was obtained by using the Wilks likelihood ratio test based on the four tetranomially distributed vectors of counts of the four different outcome combinations, one 4-vector for each of the four setting combinations. The methodology was illustrated by application to the loophole-free Bell experiments of 2015 and 2016 performed in Delft and Munich, at NIST, and in Vienna, respectively, and also to the earlier (1998) Innsbruck experiment of Weihs et al. and the recent (2022) Munich experiment of Zhang et al., which investigates the use of a loophole-free Bell experiment as part of a protocol for device-independent quantum key distribution (DIQKD).
ISSN:2673-9909
2673-9909
DOI:10.3390/appliedmath3020023