Joint measurements and Bell inequalities

Abstract

Joint quantum measurements of non-commuting observables are possible, if one accepts an increase in the measured variances. A necessary condition for a joint measurement to be possible is that a joint probability distribution exists for the measurement. This fact suggests that there may be a link with Bell inequalities, as these will be satisfied if and only if a joint probability distribution for all involved observables exists. We investigate the connections between Bell inequalities and conditions for joint quantum measurements to be possible. Mermin's inequality for the three-particle Greenberger-Horne-Zeilinger state turns out to be equivalent to the condition for a joint measurement on two out of the three quantum systems to exist. Gisin's Bell inequality for three co-planar measurement directions, meanwhile, is shown to be less strict than the condition for the corresponding joint measurement.

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• Joint measurability, steering and entropic uncertainty
• Necessary and sufficient condition for joint measurability
• Layers of classicality in the compatibility of measurements
• All incompatible measurements on qubits lead to multiparticle Bell nonlocality
• On the origin of nonclassicality in single systems
• N term pairwise correlation inequalities, steering and joint measurability
• Causality, Joint measurement and Tsirelson's bound
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• Information leak and incompatibility of physical context: A modified approach
• Operational nonlocality