Genuine entanglement measures in multipartite quantum systems

Genuine multipartite entanglement measure is an important research content and frontier problem in quantum information theory. In this paper, genuine entanglement measure for arbitrary dimensional multipartite quantum systems is constructed based on concurrence. First, the four-partite genuine entanglement measure on the basis of all possible bipartitions concurrence of the four-partite pure state is constructed. If the genuine multipartite entanglement measure can distinguish that the state $|GHZ〉$ is more entangled than the state $|W〉$, it is called a proper genuine multipartite entanglement measure. The calculation verifies that the measure given by us is not only a genuine multipartite entanglement measure, but also a proper genuine multipartite entanglement measure. Finally, the four-partite genuine entanglement measure is generalized, and the genuine entanglement measure for the arbitrary dimensional multipartite system is given. By analyzing examples, it is demonstrated that the constructed measure has good advantages. It can not only distinguish more genuine entanglement, but also give many different forms of genuine entanglement measure. Some measure constructed in literature are special cases of the measure forms in this paper.