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arXiv · 1312.2999

A Robust Mathematical Model for Clauser-Horne Experiments, With Implications for Rigorous Statistical Analysis

Peter Bierhorst
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Abstract

Recent experiments have reached detection efficiencies sufficient to close the detection loophole, testing the Clauser-Horne (CH) version of Bell's inequality. For a similar future experiment to be completely loophole-free, it will be important to have discrete experimental trials with randomized measurement settings for each trial, and the statistical analysis should not overlook the possibility of a local state varying over time with possible dependence on earlier trials (the "memory loophole"). In this paper, a mathematical model for such a CH experiment is presented, and a method for statistical analysis that is robust to memory effects is introduced. Additionally, a new method for calculating exact p-values for martingale-based statistics is described; previously, only non-sharp upper bounds derived from the Azuma-Hoeffding inequality have been available for such statistics. This improvement decreases the required number of experimental trials to demonstrate non-locality. The statistical techniques are applied to the data of recent experiments and found to perform well.

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Peter Bierhorst. 2013-12-10. A Robust Mathematical Model for Clauser-Horne Experiments, With Implications for Rigorous Statistical Analysis. https://doi.org/10.1088/1751-8113/48/19/195302

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