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

TL;DR

This paper introduces a practical scheme for classifying pure entangled states in a five-partite quantum system with dimensions 2, L, M, N, H under SLOCC, extending previous methods to more complex systems.

Contribution

It generalizes entanglement classification methods from four-partite to five-partite systems using matrix decompositions and realignment techniques.

Findings

Classified entanglement of 2×L×M×N×H systems.

Provided explicit classification for 2×2×2×2×2 five-qubit states.

Demonstrated the effectiveness of the scheme with practical examples.

Abstract

In this work we propose a practical entanglement classification scheme for pure states of $2\times L\times M\times N\times H$, under the stochastic local operation and classical communication (SLOCC), which generalizes the method explored in the entanglement classification of $2\times L\times M\times N$ to the five-partite system. The entangled states of $2\times L\times M\times N\times H$ system are first classified into different coarse-grained standard forms using matrix decompositions, and then fine-grained identification of two inequivalent entangled states with the same standard form are completed by using the matrix realignment technique. As an practical example, entanglement classes of the five-qubit system of $2\times 2\times 2\times 2\times 2$ are presented.