Detection of genuine multipartite entanglement based on local sum uncertainty relations

TL;DR

This paper introduces a new criterion based on local sum uncertainty relations for detecting genuine multipartite entanglement, demonstrating improved detection capabilities for noisy states and higher-dimensional systems.

Contribution

A novel sufficient criterion for GME detection using local sum uncertainty relations, outperforming existing methods like GME concurrence and Fisher information.

Findings

Detects more noisy W states for n=4 to 6

Successfully detects GME in 3-qutrit states

Stronger detection results than existing criteria

Abstract

Genuine multipartite entanglement (GME) offers more significant advantages in quantum information compared with entanglement. We propose a sufficient criterion for the detection of GME based on local sum uncertainty relations for chosen observables of subsystems. We apply the criterion to detect the GME properties of noisy $n$-partite W state when $n = 3, 4, 5$ and $6$, and find that the criterion can detect more noisy W states when $n$ ranges from 4 to 6. Moreover, the criterion is also used to detect the genuine entanglement of $3$-qutrit state. The result is stronger than that based on GME concurrence and fisher information.