Entanglement Properties of the Tripartite Quantum States

To study the entanglement properties of multipartite quantum states,a class of states in the tripartite quantum systems was constructed.Using the properties of the partitioned matrix,the positive matrix and the diagonally dominant matrix,applying the range criterion,the separable criterion,the structure and the partial transpositions of their density matrices were analyzed.The research shows that the states are entangled for the splits A-BC and B-AC,separable for the split AB-C.Therefore it can be concluded that the states are bound entangled for the splits A-BC and B-AC,separable with respect to the split AB-C,and finally the entanglement properties of any bipartite splits of the tripartite states are provided.