Entanglement Rényi $α$-entropy

Yu-Xin Wang, Liang-Zhu Mu, Vlatko Vedral, Heng Fan

Published 2015-04-15Version 1

Entanglement can be well quantified by R\'{e}nyi $\alpha$-entropy which is a generalization of the standard von Neumann entropy. Here we study the measure of entanglement R\'{e}nyi $\alpha$-entropy for arbitrary two-qubit states. We show that entanglement of two states may be incomparable, contrary to other well-accepted entanglement measures. These facts impose constraint on the convertibility of entangled states by local operations and classical communication. We find that when $\alpha $ is larger than a critical value, the entanglement measure by R\'{e}nyi $\alpha$-entropy is determined solely by concurrence which is a well accepted measure of entanglement. When $\alpha $ is small, the entanglement R\'{e}nyi $\alpha$-entropy of Werner state is obtained. Interestingly, we show that entanglement R\'{e}nyi $\alpha$-entropy of Werner state is always less than any pure entangled state when $\alpha $ is close to zero, even this Werner state is close to a maximally entangled state and the concurrence is larger. We also conclude that the optimal decomposition of a general mixed state cannot be the same for all $\alpha $.