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CHSH-Type Inequality Involving Commuting Continuous Variables

Instituto de Física, Universidad Nacional Autónoma de México, Mexico City A. P. 20-364, Mexico
Author to whom correspondence should be addressed.
Atoms 2019, 7(2), 46;
Received: 14 February 2019 / Revised: 21 April 2019 / Accepted: 23 April 2019 / Published: 25 April 2019
(This article belongs to the Special Issue Stochastic Electrodynamics)
PDF [298 KB, uploaded 13 May 2019]


The correlation of projections of the momentum operators of two particles is used to derive a quantum inequality for continuous variables, which must be satisfied by any bipartite system in a pure state. This inequality resembles a Clauser–Horne–Shimony–Holt (CHSH)-type inequality except for additional terms related to the imaginary component of the weak value of the momentum, which normally remains concealed in the usual quantum description but turns out to be of relevance for entangled states. Our results shed new light on the link between noncommutativity, entanglement and nonlocality of the quantum description. View Full-Text
Keywords: bipartite entanglement; weak values of linear momentum; flow and diffusive velocities; CHSH-type inequalities bipartite entanglement; weak values of linear momentum; flow and diffusive velocities; CHSH-type inequalities
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Valdés-Hernández, A.; Cetto, A.M.; de la Peña, L. CHSH-Type Inequality Involving Commuting Continuous Variables. Atoms 2019, 7, 46.

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