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Reflected Entropy Is Not a Correlation Measure by Hayden, Patrick; Lemm, Marius; Sorce, Jonathan is a scholarly article available to read on EtoBox.

What is Reflected Entropy Is Not a Correlation Measure about?

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.

Author

Hayden, Patrick; Lemm, Marius; Sorce, Jonathan

Published

2023

Language

EN