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

TL;DR

This paper extends a matrix decomposition method to classify entangled states in asymmetric tripartite quantum systems, providing practical tools and explicit examples for systems like 2×6×7.

Contribution

It generalizes the matrix decomposition method for classifying 2×M×N entangled states under SLOCC, enhancing practical applicability for asymmetric systems.

Findings

MDM is effective for classifying asymmetric tripartite states

Explicit classification example for 2×6×7 system provided

Method simplifies analysis of complex entangled states

Abstract

We extend the matrix decomposition method(MDM) in classifying the $2\times N\times N$ truly entangled states to $2\times M\times N$ system under the condition of stochastic local operations and classical communication. It is found that the MDM is quite practical and convenient in operation for the asymmetrical tripartite states, and an explicit example of the classification of $2\times 6\times 7$ quantum system is presented.