The Parametric Symmetry and Numbers of the Entangled Class of 2 \times M \times N System

TL;DR

This paper investigates the symmetry properties and counts the total number of true entangled states in the $2 imes M imes N$ tripartite system, enhancing understanding of its entanglement structure.

Contribution

It provides the first analytic expression for the total number of true entangled states and explores the symmetric properties of nonlocal parameters in this system.

Findings

Analytic formula for the number of true entangled states.

Identification of symmetric properties of nonlocal parameters.

Deeper insight into the nature of $2 imes M imes N$ entanglement.

Abstract

We present in the work two intriguing results in the entanglement classification of pure and true tripartite entangled state of $2\times M\times N$ under stochastic local operation and classical communication. (i) the internal symmetric properties of the nonlocal parameters in the continuous entangled class; (ii) the analytic expression for the total numbers of the true and pure entangled class $2\times M \times N$ states. These properties help people to know more of the nature of the $2\times M\times N$ entangled system.