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Annalen der Physik

Detection of Tripartite Genuine Entanglement by Two Bipartite Entangled States

Yize Sun, Lin Chen

Published Nov 30, 2020• 8 citations
Publisher

Abstract

Abstract There are practical motivations to construct genuine tripartite entangled states based on the collective use of two bipartite entangled states. Here, the case that the states are two‐qubit Werner states is considered. The intervals of parameters of two‐qubit Werner states are revealed such that the tripartite state is genuinely entangled. Furthermore, we also investigate the lower bound of genuine multipartite entanglement concurrence for tripartite qudit states. Several examples are given to show the effectiveness of the lower bound.

DOI
10.1002/andp.202000432

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Abstract There are practical motivations to construct genuine tripartite entangled states based on the collective use of two bipartite entangled states. Here, the case that the states are two‐qubit Werner states is considered. The intervals of parameters of two‐qubit Werner states are revealed such that the tripartite state is genuinely entangled. Furthermore, we also investigate the lower bound of genuine multipartite entanglement concurrence for tripartite qudit states. Several examples are given to show the effectiveness of the lower bound.
It is an interesting problem to construct genuine tripartite entangled states based on the collective use of two bipartite entangled states. We consider the case that the states are two-qubit Werner states, we construct the interval of parameter of Werner states such that the tripartite state is genuine entangled. Further, we present the way of detecting the tripartite genuine entanglement using current techniques in experiments. We also investigate the lower bound of genuine multipartite entanglement concurrence.
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.
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.
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.
We study multipartite entanglement and genuine tripartite entanglement based on general symmetric informationally complete positive operator valued measurements (GSIC-POVMs). By representing the bipartite density matrices in terms of GSIC-POVMs, we obtain the lower bound of the sum of squares of the corresponding probability. We then construct a special matrix with the correlation probability of GSIC-POVMs to derive useful and operational criteria to detect genuine tripartite entanglement. We also generalize the results to obtain a sufficient criterion to detect entanglement for multipartite quantum states in arbitrary dimensions. Detailed examples show that the new method can detect more entangled and genuine entangled states than previous criteria.