Max- Relative Entropy of Entanglement, alias Log Robustness

TL;DR

This paper explores the properties of the max-relative entropy of entanglement, demonstrating its equivalence to log robustness and introducing a modified version that satisfies continuity and additivity, linking it to the regularized relative entropy of entanglement.

Contribution

It establishes the equivalence between max-relative entropy of entanglement and log robustness, and proposes a modified version that is asymptotically continuous and additive.

Findings

Max-relative entropy of entanglement equals log robustness.

Modified quantity satisfies continuity and additivity.

Modified quantity equals the regularized relative entropy of entanglement.

Abstract

Properties of the max- relative entropy of entanglement are investigated, and its significance as an upper bound to the one shot rate for perfect entanglement dilution, under a particular class of quantum operations, is discussed. It is shown that it is in fact equal to another known entanglement monotone, namely the log robustness. It is known that the latter is not asymptotically continuous and it is not known whether it is weakly additive. However, by suitably modifying the max- relative entropy of entanglement we obtain a quantity which is seen to satisfy both these properties. In fact, the modified quantity is shown to be equal to the regularised relative entropy of entanglement.