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International Journal of Theoretical Physics

Revised Geometric Measure of Entanglement in Infinite Dimensional Multipartite Quantum Systems

Yinzhu Wang, Danxia Wang, Li Huang

Published May 15, 2018• 2 citations
Publisher
DOI
10.1007/s10773-018-3777-4

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We present a revised geometric measure of entanglement (RGME) which is just certain generalization of geometric measure of entanglement (GME). The revised version is an entanglement monotone. Some useful inequalities about RGME are deduced. For example, we give the formulae of RGME for the two-parameter class of states in a 2 ⊗ n quantum system, the two particles' high dimensional maximally entangled mixed state, the isotropic state including the n -particle d-level case and two multipartite bound entangled states. The results show there is a relation , and then RGME is an appropriate measure of entanglement.
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.