In this paper we give a sufficient and necessary condition under which a continuous measure (whose values belong to, the extended half-line (0,+∞) defined on a class of sets closed under the formation of intersection...In this paper we give a sufficient and necessary condition under which a continuous measure (whose values belong to, the extended half-line (0,+∞) defined on a class of sets closed under the formation of intersection can be extended to a smallest monotone class containing this class, and we also give a condition under which there exists a unique extension. In addition, we give a method by means of which a continuous measure on a monotone class can be extended again.展开更多
Based on the revised geometric measure of entanglement （RGME） proposed by us [J. Phys. A： Math. Theor. 40 （2007） 3507], we obtain the RGME of multipartite state including three-qubit GHZ state, W state, and the g...Based on the revised geometric measure of entanglement （RGME） proposed by us [J. Phys. A： Math. Theor. 40 （2007） 3507], we obtain the RGME of multipartite state including three-qubit GHZ state, W state, and the generalized Smolin state （GSS） in the presence of noise and the two-mode squeezed thermal state. Moreover, we compare their RGME with geometric measure of entanglement （GME） and relative entropy of entanglement （RE）. The results indicate RGME is an appropriate measure of entanglement. Finally, we define the Gaussian GME which is an entangled monotone.展开更多
文摘In this paper we give a sufficient and necessary condition under which a continuous measure (whose values belong to, the extended half-line (0,+∞) defined on a class of sets closed under the formation of intersection can be extended to a smallest monotone class containing this class, and we also give a condition under which there exists a unique extension. In addition, we give a method by means of which a continuous measure on a monotone class can be extended again.
基金supported by the National Natural Science Foundation of China under Grant No. 60573008
文摘Based on the revised geometric measure of entanglement （RGME） proposed by us [J. Phys. A： Math. Theor. 40 （2007） 3507], we obtain the RGME of multipartite state including three-qubit GHZ state, W state, and the generalized Smolin state （GSS） in the presence of noise and the two-mode squeezed thermal state. Moreover, we compare their RGME with geometric measure of entanglement （GME） and relative entropy of entanglement （RE）. The results indicate RGME is an appropriate measure of entanglement. Finally, we define the Gaussian GME which is an entangled monotone.
