On genuine entanglement for tripartite systems

TL;DR

This paper develops new criteria based on partial transposition and correlation tensor norms to detect genuine tripartite entanglement, improving detection capabilities over previous methods.

Contribution

It introduces analytical criteria for genuine entanglement detection in tripartite qubit and qudit systems, enhancing existing detection techniques.

Findings

More genuine tripartite entangled states are detected compared to previous methods.

Criteria are applicable to both qubit and qudit systems.

Analytical and tensor-based methods improve detection accuracy.

Abstract

We investigate the genuine entanglement in tripartite systems based on partial transposition and the norm of correlation tensors of the density matrices. We first derive an analytical sufficient criterion to detect genuine entanglement of tripartite qubit quantum states combining with the partial transposition of the density matrices. Then we use the norm of correlation tensors to study genuine entanglement for tripartite qudit quantum states and obtain a genuine entanglement criterion by constructing certain matrices. With detailed examples our results are seen to be able to detect more genuine tripartite entangled states than previous studies.