Detection and measure of genuine tripartite entanglement with partial transposition and realignment of density matrices

TL;DR

This paper introduces new criteria based on partial transposition and realignment of density matrices to effectively detect and quantify genuine tripartite entanglement, enhancing existing bipartite entanglement tools.

Contribution

It develops sufficient conditions and lower bounds for genuine tripartite entanglement using PPT and realignment criteria, extending bipartite methods to multipartite systems.

Findings

Provides effective criteria for detecting genuine tripartite entanglement.

Derives lower bounds for tripartite entanglement concurrence.

Extends bipartite entanglement detection methods to multipartite systems.

Abstract

It is challenging task to detect and measure genuine multipartite entanglement. We investigate the problem by considering the average based positive partial transposition(PPT) criterion and the realignment criterion. Sufficient conditions for detecting genuine tripartite entanglement are presented. We also derive lower bounds for the genuine tripartite entanglement concurrence with respect to the conditions. While the PPT criterion and the realignment criterion are powerful for detecting bipartite entanglement and for providing lower bounds of bipartite concurrences, our results give an effective operational way to detect and measure the genuine tripartite entanglement.