三体量子态的纠缠性质

为了研究多体量子态的纠缠性质,构造了一类三体量子态.利用矩阵分析理论中的分块矩阵、正矩阵、对角占优矩阵的性质,运用量子信息中的值域判据、可分判据,研究了密度矩阵的结构和部分转置;证明了在分割ABC和B-AC下密度矩阵是纠缠的,在分割AB-C下密度矩阵是可分的.由此得到在分割A-BC和B-AC下,量子态是束缚纠缠态,在分割AB-C下量子态是可分态,给出了一类三体量子态在任意两体分割上的纠缠性质.

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.