Entanglement classification of 2 X 2 X 2 X d quantum systems via the ranks of the multiple coefficient matrices

TL;DR

This paper introduces a comprehensive method for classifying entanglement in 2 x 2 x 2 x d quantum systems by analyzing the ranks of coefficient matrices, enhancing understanding of multipartite entanglement.

Contribution

It extends entanglement classification techniques to arbitrary-dimensional multipartite pure states using coefficient matrix ranks, specifically applied to 2 x 2 x 2 x d systems.

Findings

Provides a systematic classification procedure based on matrix ranks.

Applies the method to specific 2 x 2 x 2 x d quantum systems.

Enhances the toolkit for entanglement analysis in complex quantum systems.

Abstract

The coefficient matrix is an efficient tool in entanglement classification under stochastic local operation and classical communication. In this work, we take all the ranks of the coefficient matrices into account in the method of entanglement classification, and give the entanglement classification procedure for arbitrary-dimensional multipartite pure states under stochastic local operation and classical communication. As a main application, we study the entanglement classification for quantum systems in the Hilbert space ${\cal H} = \mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^d$ in terms of the ranks of the coefficient matrices.