Leggett–Garg-like Inequalities from a Correlation Matrix Construction

The Leggett–Garg Inequality (LGI) constrains, under certain fundamental assumptions, the correlations between measurements of a quantity <i>Q</i> at different times. Here, we analyze the LGI and propose similar but somewhat more elaborate inequalities, employing a technique that utilizes...

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Bibliographic Details
Published in:Quantum Reports
Main Authors: Dana Ben Porath, Eliahu Cohen
Format: Article
Language:English
Published: MDPI AG 2023-04-01
Subjects:
Online Access:https://www.mdpi.com/2624-960X/5/2/25
Description
Summary:The Leggett–Garg Inequality (LGI) constrains, under certain fundamental assumptions, the correlations between measurements of a quantity <i>Q</i> 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.
ISSN:2624-960X