Joint measurements and Bell inequalities

Wonmin Son, Anna Erika Elisabeth Andersson, Stephen M Barnett, M S Kim

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Abstract

Joint quantum measurements of noncommuting 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 coplanar measurement directions, meanwhile, is shown to be less strict than the condition for the corresponding joint measurement.

Original languageEnglish
Article number052116
Number of pages7
JournalPhysical Review A
Volume72
Issue number5
DOIs
Publication statusPublished - Nov 2005

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