Separability and entanglement in tripartite states

Miao Xu, Weifeng Zhou, Feng Chen +2 more

Abstract A quantum entangled state is easily disturbed by noise and degenerates into a separable state. Compared to the entanglement with bipartite quantum systems, less progress has been made for the entanglement with multipartite quantum systems. For tripartite separability of a four-qubit system, we propose two entanglement witnesses, each of which corresponds to a necessary condition of tripartite separability. For the four-qubit GHZ state mixed with a W state and white noise, we prove that the necessary conditions of tripartite separability are also sufficient at W states side.

George Jaroszkiewicz

George Jaroszkiewicz

Hui Zhao, Yu-Qiu Liu, Zhi‐Xi Wang +1 more

We study the classification of entanglement in tripartite systems by using Bell-type inequalities and principal basis. By using Bell unctions and the generalized three dimensional Pauli operators, we present a set of Bell inequalities which classifies the entanglement of triqutrit fully separable and bi-separable mixed states. By using the correlation tensors in the principal basis representation of density matrices, we obtain separability criteria for fully separable and bi-separable 2 ⊗ 2 ⊗ 3 quantum mixed states. Detailed example is given to illustrate our criteria in classifying the tripartite entanglement.

Kiara Hansenne

Zhao Hu

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.