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

TL;DR

This paper introduces a new method for classifying multipartite entangled states in $2 imes N imes N$ systems, enabling direct classification without lower-dimensional references and explaining persistent non-local parameters for $N \,\geq\, 4$.

Contribution

The authors present a novel classification approach for $2 imes N imes N$ entangled states that simplifies the process and provides insights into non-local parameters.

Findings

All inequivalent classes of true entangled states can be directly classified.

The method works for any dimension N without prior lower-dimensional classification.

It explains the presence of non-local parameters in entanglement classes for N ≥ 4.

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 $N\geq 4$ .