Volume 534, Issue 11 2200289
Research Article

A Characterization of Entangled Two-Qubit States via Partial-Transpose-Moments

Lin Zhang

Corresponding Author

Lin Zhang

School of Science, Hangzhou Dianzi University, Hangzhou, 310018 P. R. China

E-mail: [email protected]; [email protected]; [email protected]

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Ming-Jing Zhao

Ming-Jing Zhao

School of Science, Beijing Information Science and Technology University, Beijing, 100192 P. R. China

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Lin Chen

Corresponding Author

Lin Chen

School of Mathematical Sciences, Beihang University, Beijing, 100191 China

International Research Institute for Multidisciplinary Science, Beihang University, Beijing, 100191 China

E-mail: [email protected]; [email protected]; [email protected]

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Hua Xiang

Hua Xiang

School of Mathematics and Statistics, Wuhan University, Wuhan, 430072 P. R. China

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Yi Shen

Corresponding Author

Yi Shen

School of Science, Jiangnan University, Wuxi, Jiangsu, 214122 P. R. China

E-mail: [email protected]; [email protected]; [email protected]

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First published: 10 September 2022

Abstract

Although quantum entanglement is an important resource, its characterization is quite challenging. The partial transposition is a common method to detect bipartite entanglement. In this paper, the authors study the partial-transpose(PT)-moments of two-qubit states, and completely describe the whole region, composed of the second and third PT-moments, for all two-qubit states. Furthermore, they determine the accurate region corresponding to all entangled two-qubit states. The states corresponding to those boundary points of the whole region, and to the border lines between separable and entangled states are analyzed. As an application, they characterize the entangled region of PT-moments for the two families of Werner states and Bell-diagonal states. The relations between entanglement and the pairs of PT-moments are revealed from these typical examples. They also numerically plot the whole region of possible PT-moments for all two-qubit X-states, and find that this region is almost the same as the whole region of PT-moments for all two-qubit states. Moreover, they extend their results to detect the entanglement of multiqubit states. By utilizing the PT-moment-based method to characterize the entanglement of the multiqubit states mixed by the GHZ and W states, they propose an operational way of verifying the genuine entanglement in such states.

Conflict of Interest

The authors declare no conflict of interest.

Data Availability Statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

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