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Tightening monogamy and polygamy relations of unified entanglement in multipartite systems

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Abstract

We study monogamy and polygamy inequalities of unified entanglement in multipartite quantum systems. We first derive the monogamy inequality of unified-(q, s) entanglement for multi-qubit states under arbitrary bipartition, and then obtain the monogamy inequalities of the \(\alpha \)th (\(0\le \alpha \le \frac{r}{2}, r\ge \sqrt{2}\)) power of entanglement of formation for tripartite states and their generalizations in multi-qubit quantum states. We also generalize the polygamy inequalities of unified-(q, s) entanglement for multi-qubit states under arbitrary bipartition. Moreover, we investigate polygamy inequalities of the \(\beta \)th (\(\beta \ge \mathrm{max}\{1, s\}, 0\le s\le s_0, 0\le s_0\le \sqrt{2}\)) power of the entanglement of formation for \(2\otimes 2\otimes 2\) and n-qubit quantum systems. Finally, using detailed examples, we show that the results are tighter than previous studies.

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Acknowledgements

This work is partially supported by Simons Foundation grant no. 523868 and National Natural Science Foundation of China grant no. 12126351.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Mei-Ming Zhang & Naihuan Jing

  2. Department of Mathematics, North Carolina State University, Raleigh, NC, 27695, USA

    Naihuan Jing

  3. Department of Mathematics, Faculty of Science, Beijing University of Technology, Beijing, 100124, China

    Hui Zhao

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  1. Mei-Ming Zhang
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  2. Naihuan Jing
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Correspondence to Naihuan Jing.

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Zhang, MM., Jing, N. & Zhao, H. Tightening monogamy and polygamy relations of unified entanglement in multipartite systems. Quantum Inf Process 21, 136 (2022). https://doi.org/10.1007/s11128-022-03479-9

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