Classification of the Entangled States of $2 \times N \times N$

Abstract

We develop a novel method in classifying the multipartite entanglement state of $2\times N\times N$ under stochastic local operation and classical communication. In this method, all inequivalent classes of true entangled state can be assorted directly without knowing the classification information of lower dimension ones for any given dimension $N$. It also gives a nature explanation for the non-local parameters remaining in the entanglement classes while $N\geq 4$ .