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arXiv:1711.05041 · Physical Review A

Measure and detection of genuine multipartite entanglement for tripartite systems

Ming Li, Lingxia Jia, Jing Wang, Shu‐Qian Shen, Shao-Ming Fei

Published Nov 13, 2017• 36 citations
arXivHTMLPDF

Abstract

It is a computationally hard task to certify genuine multipartite entanglement (GME). We investigate the relation between the norms of the correlation vectors and the detection of GME for tripartite quantum systems. A sufficient condition for GME and an effective lower bound for the GME concurrence are derived. Several examples are considered to show the effectiveness of the criterion and the lower bound of GME concurrence.

DOI
10.1103/physreva.96.052314

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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.
The problems of genuine multipartite entanglement detection and classification are challenging. We show that a multipartite quantum state is genuine multipartite entangled if the multipartite concurrence is larger than certain quantities given by the number and the dimension of the subsystems. This result also provides a classification of various genuine multipartite entanglements. We present a lower bound of the multipartite concurrence in terms of bipartite concurrences. While various operational approaches are available for providing lower bounds of bipartite concurrences, our results give an effective operational way to detect and classify genuine multipartite entanglement. As applications, genuine multipartite entanglement of tripartite systems is analyzed in detail.
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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 nnn-partite W state when n=3,4,5n = 3, 4, 5n=3,4,5 and 666, and find that the criterion can detect more noisy W states when nnn ranges from 4 to 6. Moreover, the criterion is also used to detect the genuine entanglement of 333-qutrit state. The result is stronger than that based on GME concurrence and fisher information.