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 $S_R^{\left(\alpha \right)}$ 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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• Quantum correlations in quantum information
• Quantum correlations, foundations & formalism
• Quantum information theory