A Rigorous Analysis of the Clauser-Horne-Shimony-Holt Inequality Experiment When Trials Need Not Be Independent

Abstract

The Clauser-Horne-Shimony-Holt (CHSH) inequality is a constraint that local theories must obey. Quantum Mechanics predicts a violation of this inequality in certain experimental settings. Treatments of this subject frequently make simplifying assumptions about the probability spaces available to a local hidden variable theory, such as assuming the state of the system is a discrete or absolutely continuous random variable, or assuming that repeated experimental trials are independent and identically distributed. In this paper, we do two things: first, show that the CHSH inequality holds even for completely general state variables in the measure-theoretic setting, and second, demonstrate how to drop the assumption of independence of subsequent trials while still being able to perform a hypothesis test that will distinguish Quantum Mechanics from local theories. The statistical strength of such a test is computed.

23 pages, 2 figures. To appear in Foundations of Physics

References in corpus (3)

• Device-independent security of quantum cryptography against collective attacks
• Beyond Bell's Theorem: Correlation Scenarios
• A Classification of Hidden-Variable Properties

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• A Robust Mathematical Model for Clauser-Horne Experiments, With Implications for Rigorous Statistical Analysis
• Test of the no-signaling principle in the Hensen "loophole-free CHSH experiment"
• (Nearly) optimal P-values for all Bell inequalities
• Bell nonlocality with a single shot
• Eberhardt's inequality and recent loophole-free experiments