Leggett–Garg-like Inequalities from a Correlation Matrix Construction

Dana Ben Porath; Eliahu Cohen

doi:10.3390/quantum5020025

Leggett–Garg-like Inequalities from a Correlation Matrix Construction

Dana Ben Porath, Eliahu Cohen

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The Leggett–Garg Inequality (LGI) constrains, under certain fundamental assumptions, the correlations between measurements of a quantity Q at different times. Here, we analyze the LGI and propose similar but somewhat more elaborate inequalities, employing a technique that utilizes the mathematical properties of correlation matrices, which was recently proposed in the context of nonlocal correlations. We also find that this technique can be applied to inequalities that combine correlations between different times (as in LGI) and correlations between different locations (as in Bell inequalities). All the proposed bounds include additional correlations compared to the original ones and also lead to a particular form of complementarity. A possible experimental realization and some applications are briefly discussed.

Original language	English
Pages (from-to)	398-406
Number of pages	9
Journal	Quantum Reports
Volume	5
Issue number	2
DOIs	https://doi.org/10.3390/quantum5020025
State	Published - Jun 2023

Bibliographical note

Publisher Copyright:
© 2023 by the authors.

Funding

E.C. was supported by the Israeli Innovation Authority under Project 73795 and the Eureka program, by Elta Systems Ltd., by the Pazy Foundation, by the Israeli Ministry of Science and Technology, and by the Quantum Science and Technology Program of the Israeli Council of Higher Education.

Funders	Funder number
Elta Systems Ltd.
Quantum Science and Technology Program of the Israeli Council of Higher Education
Ministry of science and technology, Israel
PAZY Foundation
Israel Innovation Authority	73795

Keywords

Bell–Leggett–Garg Inequality
Leggett–Garg Inequality
foundations of quantum mechanics
quantum correlations
quantum information

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Leggett–Garg-like Inequalities from a Correlation Matrix Construction

Abstract

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