Multipartite Entanglement Measure

In this paper, we generalize the residual entanglement to the case of multipartite states in arbitrary dimensions by making use of a new method. Through the introduction of a special entanglement measure, the residual entanglement of mixed states takes on a form that is more elegant than that in Ref.[7] (Phys.Rev.A 61 (2000) 052306) . The result obtained in this paper is different from the previous one given in Ref.[8] (Phys.Rev.A 63 (2000) 044301). Several examples demonstrate that our present result is a good measurement of the multipartite entanglement. Furthermore, the original residual entanglement is a special case of our result.