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Acta Physica Sinica

Negative quantum conditional entropy and the entanglement measure of a kind of mixed state of bipartite quantum system

Zhou Bing-Ju, Xiaojuan Liu, Mao-Fa Fang, Zhou Qing-Ping, Mingwei Liu, (1)湖南科技大学物理学院，湘潭 411201; (2)湖南科技大学物理学院，湘潭 411201;湖南师范大学物理与信息学院，长沙 410081;中国科学院安徽光学精密机械研究所，合肥 230031; (3)湖南师范大学物理与信息学院，长沙 410081;中国科学院安徽光学精密机械研究所，合肥 230031

Published Jan 1, 2007• 0 citations

Abstract

From negative quantum conditional entropy point of view this paper intestigates the entanglement measure of the prue state and a kind of mixed state of bipartite quantum system. Also this paper gives a definition of quantum conditional entropy of entanglement EA｜B(ρAB) and proves that it satisfies the four fundamental conditions of a entanglement measure for a kind of mixed state of 2×2 quantum system by this negative quantum conditional entropy Using conditional entropy of entanglement, this paper investigates the quantum entanglement between the two identical two-level atoms simultaneously interacting with vacuum cavity field as an application. This paper compares conditional entropy of entanglement and concurrence at the same condition, and the result shows that the curves of their evolvements are identical. These obtained results test and verifys that conditions of an entanglement measure may be taken as the entanglement measure of the prue state and a kind of mixed state of bipartite quantum system.

DOI: 10.7498/aps.56.3937

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In this paper we investigate two different entanglement measures in the case of mixed states of two qubits. We prove that the negativity of a state can never exceed its concurrence and is always larger than √[(1 − C ) 2 + C 2 ] − (1 − C ), where C is the concurrence of the state. Furthermore, we derive an explicit expression for the states for which the upper or lower bound is satisfied. Finally we show that similar results hold if the relative entropy of entanglement and the entanglement of formation are compared.

Any arbitrary state in bipartite quantum system can be transformed into a two-parameter class of states by means of local quantum operation and classical communication.In this paper,the quantum relative entropy of entanglement for this kind of states is calculated,the nearest separable states are found and the analytic expression of the entanglement is obtained.The comparation with two other measures of entanglement,the negativity and the entanglement of formation,is also made.The sequence of three measures from high to low is the negativity,the entanglement of formation and the relative entropy of entanglement.

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