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.

Close

PrevNext

View figure in article

• 

• Quantum correlations in quantum information
• Quantum correlations, foundations & formalism
• Quantum information theory