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Laser Physics Letters

An improved lower bound of genuine tripartite entanglement concurrence

Jing Wang, Xue‐Na Zhu, Ming Li, Shu‐Qian Shen, Shao-Ming Fei

Published Oct 22, 2021• 3 citations
Publisher

Abstract

Abstract As one of the important types of entanglement, genuine multipartite entanglement (GME) offers significant advantages in many quantum information processing tasks. We study the GME concurrence and present an improved lower bound of the GME concurrence for tripartite systems, which is shown to be much tighter than some existing ones. We show by detailed example that our new bound can detect more genuine tripartite entangled states. While it is a formidable task to compute the genuine tripartite entanglement concurrence analytically, our results give an effective operational way to estimate the genuine tripartite entanglement.

DOI
10.1088/1612-202x/ac2eed

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Abstract As one of the important types of entanglement, genuine multipartite entanglement (GME) offers significant advantages in many quantum information processing tasks. We study the GME concurrence and present an improved lower bound of the GME concurrence for tripartite systems, which is shown to be much tighter than some existing ones. We show by detailed example that our new bound can detect more genuine tripartite entangled states. While it is a formidable task to compute the genuine tripartite entanglement concurrence analytically, our results give an effective operational way to estimate 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.
Genuine multipartite entanglement (GME) represents the strongest form of entanglement in multipartite systems, providing significant advantages in various quantum information processing tasks. In this work, we propose an experimentally feasible scheme for detecting GME, based on the truncated moments of positive maps. Our method avoids the need for full state tomography, making it scalable for larger systems. We provide illustrative examples of both pure and mixed states to demonstrate the efficacy of our formalism in detecting inequivalent classes of tripartite genuine entanglement. We further demonstrate the detection of quadripartite genuine entanglement, underscoring the effectiveness of our method in identifying entanglement beyond the tripartite case. Finally, we present a proposal for realizing these moments in real experiments.
Although genuine multipartite entanglement (GME), as one quantum resource, is indispensable in quantum information processing, most of the existing measures cannot detect GME faithfully. In this paper we present a GME measure, namely, the minimum pairwise concurrence (MPC), by introducing pairwise entanglement, which characterizes the entanglement between two single-qubit subsystems of a multipartite system without tracing out the remaining qubit. The pairwise entanglement can be obtained by combining the entanglement of the reduced subsystem and the three-tangle. Compared with existing measures, the MPC measure outperforms the previous ones in many aspects. Due to its fine properties, it thus is believed that the MPC could be a good candidate for achieving potential quantum tasks and also could facilitate the understanding of GME.
As one of the important types of entanglement, genuine multipartite entanglement plays a key role in both foundational and practical aspects of quantum information theory. In this manuscript, we study the genuine multipartite entanglement in tripartite quantum systems based on the enhanced realignment criterion. A family of sufficient conditions for detecting genuine tripartite entanglement are presented. Moreover, lower bounds of the genuine multipartite entanglement concurrence are derived. The detection power and advantages of our results are illustrated through several examples.