Revised Geometric Measure of Entanglement in Infinite Dimensional Multipartite Quantum Systems

In Cao and Wang (J. Phys.: Math. Theor. 40 , 3507–3542, 2007 ), the revised geometric measure of entanglement (RGME) for states in finite dimensional bipartite quantum systems was proposed. Furthermore, in Cao and Wang (Commun. Theor. Phys. 51 (4), 613–620, 2009 ), the authors obtained the revised geometry measure of entanglement for multipartite states including three-qubit GHZ state, W state, and the generalized Smolin state in the presence of noise and the two-mode squeezed thermal state, and defined the Gaussian geometric entanglement measure. In this paper, we generalize the RGME to infinite dimensional multipartite quantum systems, and prove that this measure satisfies some necessary properties as a well-defined entanglement measure, including monotonicity under local operations and classical communications.