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General monogamy and polygamy properties of quantum systems

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Abstract

Monogamy and polygamy are important properties of entanglement, which characterize the entanglement distribution of multipartite systems. We study general monogamy and polygamy relations based on the \(\alpha \)th \((0\le \alpha \le \gamma )\) power of entanglement measures and the \(\beta \)th \((\beta \ge \delta )\) power of assisted entanglement measures, respectively. We illustrate that these monogamy and polygamy relations are tighter than the inequalities in the article Jin et al. (Quantum Inf Process 19:101, 2020), so that the entanglement distribution can be more precisely described for entanglement states that satisfy stronger constraints. For specific entanglement measures such as concurrence and the convex-roof extended negativity, by applying these relations, one can yield the corresponding monogamous and polygamous inequalities, which take the existing ones in the articles Zhu and Fei (Quantum Inf Process 18:23, 2019) and Jin et al. (Quantum Inf Process 18:105, 2019) as special cases. More details are presented in the examples.

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Acknowledgements

This work is supported by the NSF of China under Grant Nos. 12175147, 12171044.

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Authors and Affiliations

  1. Department of Mathematics, East China University of Technology, Nanchang, 330013, People’s Republic of China

    Bing Xie

  2. School of Science, Beijing Information Science and Technology University, Beijing, 100192, People’s Republic of China

    Ming-Jing Zhao

  3. School of Computer and Computing Science, Zhejiang University City College, Hangzhou, 310015, People’s Republic of China

    Bo Li

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  1. Bing Xie
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Correspondence to Bo Li.

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Xie, B., Zhao, MJ. & Li, B. General monogamy and polygamy properties of quantum systems. Quantum Inf Process 22, 124 (2023). https://doi.org/10.1007/s11128-023-03861-1

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