Efficient quantification of experimental evidence against local realism

Abstract

Tests of local realism and their applications aim for very high confidence in their results even in the presence of potentially adversarial effects. For this purpose, one can measure a quantity that reflects the amount of violation of local realism and determine a bound on the probability, according to local realism, of obtaining a violation at least that observed. In general, it is difficult to obtain sufficiently robust and small bounds. Here we describe an efficient protocol for computing such bounds from any set of Bell inequalities for any number of parties, measurement settings, or outcomes. The protocol can be applied to tests of other properties (such as entanglement or dimensionality) that are witnessed by linear inequalities.

9 pages, 3 figures

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• Bell nonlocality with a single shot
• Bounding the plausibility of physical theories in a device-independent setting via hypothesis testing
• Geometric Decompositions of Bell Polytopes with Practical Applications
• Bell Inequalities for Continuously Emitting Sources
• Analysis of Coincidence-Time Loopholes in Experimental Bell Tests
• A Rigorous Analysis of the Clauser-Horne-Shimony-Holt Inequality Experiment When Trials Need Not Be Independent
• Corrected Bell and Noncontextuality Inequalities for Realistic Experiments
• Eberhardt's inequality and recent loophole-free experiments
• Memory attacks in network nonlocality and self-testing
• Device-independent certification of desirable properties with a confidence interval
• Performance of Test Supermartingale Confidence Intervals for the Success Probability of Bernoulli Trials
• Strength of statistical evidence for genuine tripartite nonlocality