Classification of Bipartite and Tripartite Qutrit Entanglement Under SLOCC

Xiangrong Li, Dafa Li

Guoying Lu, Pan Feng, (1)辽宁师范大学物理系，大连 116029; (2)辽宁师范大学物理系，大连 116029;辽宁大学物理系，沈阳 110036

Classification and quantification of bipartite qubit, tripartite qubit, and bipartite qutrit entanglement are studied in detail based on the entanglement measure of multipartite pure states. The results show that different ways of pure state entanglement can be characterized by extremal values of the corresponding entanglement measure under the stochastic local operation and classical communication(SLOCC). Detailed analysis shows that there are three different kinds of entanglement under the SLOCC in both tripartite qubit and bipartite qutrit pure state systems. Comparison of the measure with the recently proposed entropy-product measure is made and briefly discussed.

Bernhard Baumgartner, Beatrix C. Hiesmayr, Heide Narnhofer

Guo‐Qiang Zhu, Xuean Zhao, You‐Quan Li

Yang Xin-Gang, Wang Zhi-Xi, Wang Xiao-Hong +1 more

We classify biqutrit and triqutrit pure states under stochastic local operations and classical communication. By investigating the right singular vector spaces of the coefficient matrices of the states, we obtain explicitly two equivalent classes of biqutrit states and twelve equivalent classes of triqutrit states respectively.

S. M. Zangi, Junli Li, Cong‐Feng Qiao

Abstract We present a practical classification scheme for the four-partite entangled states under stochastic local operations and classical communication (SLOCC). By transforming a four-partite state into a triple-state set composed of two tripartite states and a bipartite state, the entanglement classification is reduced to the classification of tripartite and bipartite entanglements. This reduction method has the merit of involving only the linear constrains, and meanwhile provides an insight into the entanglement character of the subsystems.