Classification of the Entangled states L\times N\times N

Jun-Li Li, Shi-Yuan Li, Cong-Feng Qiao

Published 2011-08-29, updated 2012-02-02Version 2

We presented a general classification scheme for the tripartite $L\times N\times N$ entangled system under stochastic local operation and classical communication. The whole classification procedure consists of two correlated parts: the simultaneous similarity transformation of a commuting matrix pair into a canonical form and the study of internal symmetry of parameters in the canonical form. Based on this scheme, a concrete example of entanglement classification for a $3\times N\times N$ system is given.