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arXiv:2209.04768 · International Journal of Quantum Information

On genuine entanglement for tripartite systems

Hui Zhao, Lin Liu, Zhi‐Xi Wang, Naihuan Jing, Jing Li

Published Jan 21, 2022• 3 citations
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Abstract

In this paper, we investigate the genuine entanglement in tripartite systems based on partial transposition and the norm of correlation tensors of the density matrices. We first derive an analytical sufficient criterion to detect genuine entanglement of tripartite qubit states combining with the partial transposition of the density matrices. Then, we use the norm of correlation tensors to study genuine entanglement for tripartite qudit quantum states and obtain a genuine entanglement criterion by constructing certain matrices. With detailed examples, our results are seen to be able to detect more genuine tripartite entangled states than previous studies.

DOI
10.1142/s0219749921500386

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In this paper, we investigate the genuine entanglement in tripartite systems based on partial transposition and the norm of correlation tensors of the density matrices. We first derive an analytical sufficient criterion to detect genuine entanglement of tripartite qubit states combining with the partial transposition of the density matrices. Then, we use the norm of correlation tensors to study genuine entanglement for tripartite qudit quantum states and obtain a genuine entanglement criterion by constructing certain matrices. With detailed examples, our results are seen to be able to detect more genuine tripartite entangled states than previous studies.
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.
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.
Abstract We study the genuine multipartite entanglement in tripartite quantum systems by using the principal basis matrix representations of density matrices. Using the Schmidt decomposition and local unitary transformation, we first convert the general states to simpler forms and then construct some special matrices from the correlation tensors of the simplified density matrices. Based on the different linear combinations of these matrices, necessary conditions are presented to detect genuine multipartite entanglement of tripartite states. Detailed examples show that our method can detect more entangled states than previous ones.
We study the genuine multipartite entanglement of arbitrary n-partite quantum states by representing the density matrices in terms of the generalized Pauli operators. We introduce a general framework for detecting genuine multipartite entanglement and non full-separability of multipartite quantum states with arbitrary dimensions based on correlation tensors. Effective criterion is derived to verify the genuine multipartite entanglement. Detailed examples are given to show that the criterion detects more genuine multipartite entanglement than the existing criteria.
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.