Reflected entropy is not a correlation measure

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 Rényi 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.

v1 is 4 pages long; v2 contains light edits to bring the preprint in line with the published version, and is 4.5 pages long

References in corpus (3)

• Universal tripartite entanglement in one-dimensional many-body systems
• Multipartite Reflected Entropy
• Entanglement Wedge Cross Section Inequalities from Replicated Geometries