Better Bell inequalities (passion at a distance)

Abstract

I explain so-called quantum nonlocality experiments and discuss how to optimize them. Statistical tools from missing data maximum likelihood are crucial. New results are given on CGLMP, CH and ladder inequalities. Open problems are also discussed.

Published at http://dx.doi.org/10.1214/074921707000000328 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (13)

• Bell inequalities for arbitrarily high dimensional systems
• Bounding the set of quantum correlations
• State estimation for large ensembles
• Grothendieck's constant and local models for noisy entangled quantum states
• Maximal violation of the CGLMP inequality for infinite dimensional states
• Bell's inequality and the coincidence-time loophole
• Optimal Bell tests do not require maximally entangled states
• Bell's theorem and the experiments: Increasing empirical support to local realism
• Time, Finite Statistics, and Bell's Fifth Position
• No time loophole in Bell's theorem; the Hess-Philipp model is non-local
• Comment on "Exclusion of time in the theorem of Bell" by K. Hess and W. Philipp
• Teleportation into Quantum Statistics
• On Quantum Statistical Inference, II

Cited by in corpus (5)

• Maximal violation of the CGLMP inequality for infinite dimensional states
• Statistics, Causality and Bell's Theorem
• Increasing the statistical significance of entanglement detection in experiments
• Bell Inequalities, Experimental Protocols and Contextuality
• A proof of Bell's inequality in quantum mechanics using causal interactions