Detection of tripartite entanglement based on principal basis matrix representations

TL;DR

This paper introduces a novel method for detecting tripartite entanglement in quantum systems using principal basis matrix representations, which improves detection capabilities over previous techniques.

Contribution

It develops a new approach based on principal basis matrices and correlation tensors, enhancing entanglement detection in tripartite quantum states.

Findings

Detects more entangled states than previous methods

Utilizes Schmidt decomposition and local unitaries for simplification

Provides detailed examples demonstrating effectiveness

Abstract

We study the entanglement in tripartite quantum systems by using the principal basis matrix representations of density matrices. Using the Schmidt decomposition and local unitary transformation, we first convert the general states to simpler forms and then construct some special matrices from the correlation tensors of the simplified density matrices. Based on the different linear combinations of these matrices, necessary conditions are presented to detect entanglement of tripartite states. Detailed examples show that our method can detect more entangled states than previous ones.