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Bayesian analysis of Bell inequalities

Asher Peres
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Abstract

Statistical tests are needed to determine experimentally whether a hypothetical theory based on local realism can be an acceptable alternative to quantum mechanics. It is impossible to rule out local realism by a single test, as often claimed erroneously. The ``strength'' of a particular Bell inequality is measured by the number of trials that are needed to invalidate local realism at a given confidence level. Various versions of Bell's inequality are compared from this point of view. It is shown that Mermin's inequality for Greenberger-Horne-Zeilinger states requires fewer tests than the Clauser-Horne-Shimony-Holt inequality or than its chained variants applied to a singlet state, and also than Hardy's proof of nonlocality.

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Asher Peres. 1999-05-25. Bayesian analysis of Bell inequalities. https://doi.org/10.1002/(sici)1521-3978(200005)48%3A5%2F7%3C531%3A%3Aaid-prop531%3E3.0.co%3B2-%23

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