Global Entanglement for Multipartite Quantum States

Based on the residual entanglement [9] (Phys. Rev. A \textbf{71}, 044301 (2005)), we present the global entanglement for a multipartite quantum state. The measure is shown to be also obtained by the bipartite partitions of the multipartite state. The distinct characteristic of the global entanglement is that it consists of the sum of different entanglement contributions. The measure can provide sufficient and necessary condition of fully separability for pure states and be conveniently extended to mixed states by minimizing the convex hull. To test the sufficiency of the measure for mixed states, we evaluate the global entanglement of bound entangled states. The properties of the measure discussed finally show the global entanglement is an entanglement monotone.