Reflected entropy is not a correlation measure

• URL: http://arxiv.org/abs/2302.10208v2
• Date: Wed, 7 Jun 2023 10:14:14 GMT
• Title: Reflected entropy is not a correlation measure
• Abstract summary: We show that the "reflected entropy" defined by Dutta and Faulkner is not monotonically decreasing under partial trace. Our counterexamples show that none of the R'enyi reflected entropies $S_R(alpha)$ for $0 alpha 2$ is a correlation measure.
• Score: 1.1470070927586016
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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