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arXiv · 2302.10208

Reflected entropy is not a correlation measure

Patrick Hayden·Marius Lemm·Jonathan Sorce
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Abstract

By explicit counterexample, we show that the "reflected entropy" defined by Dutta and Faulkner is not monotonically decreasing under partial trace, and so is not a measure of physical correlations. In fact, our counterexamples show that none of the R\'enyi reflected entropies $S_{R}^{(\alpha)}$ for $0 < \alpha < 2$ is a correlation measure; the usual reflected entropy is realized as the $\alpha=1$ member of this family. The counterexamples are given by quantum states that correspond to classical probability distributions, so reflected entropy fails to measure correlations even at the classical level.

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Patrick Hayden, Marius Lemm, Jonathan Sorce. 2023-02-20. Reflected entropy is not a correlation measure. https://doi.org/10.1103/physreva.107.l050401

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