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 different 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] used by Coffman [Phys. Rev. A 61, 052306 (2000)]. The result obtained in this paper is different from the previous one given in Ref. [8] by Wong and Christensen [Phys. Rev. A 63, 044301 (2000)]. 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.