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Polygamy relations for tripartite and multipartite quantum systems

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Abstract

We study the polygamy property in tripartite and multipartite quantum systems. In tripartite system, we build a solution set for polygamy in tripartite system and find a sufficient and necessary condition of the set for continuous measure of quantum correlation Q to be polygamous. In multipartite system, we provide generalized definitions for polygamy in n-qubit systems with \(n\ge 4\), and then, we build polygamy inequalities with a polygamy power \(\beta \). Next we also describe that any entanglement of assistance can be polygamy according to our new definition in multipartite systems. For better understanding, we use right triangle and tetrahedron to explain our new polygamy relations. Moreover, the polygamy relations between each single qubit and its remaining partners are also investigated to enrich our results.

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Acknowledgements

This work is supported by the Young Doctoral Program Embarks of Guangzhou (No. 2024A04J4450). This work is also supported by the Key Lab of Guangzhou for Quantum Precision Measurement under Grant No. 202201000010 and the Key Research and Development Project of Guangdong Province under Grant No. 2020B0303300001.

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Authors and Affiliations

  1. College of Mathematics and Informatics, South China Agricultural University, Guangzhou, 510642, China

    Yanying Liang & Haozhen Situ

  2. School of Mathematics, South China University of Technology, Guangzhou, 510641, China

    Zhu-Jun Zheng

  3. Laboratory of Quantum Science and Engineering, South China University of Technology, Guangzhou, 510642, China

    Zhu-Jun Zheng

Authors
  1. Yanying Liang
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  2. Haozhen Situ
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  3. Zhu-Jun Zheng
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Yanying Liang wrote the main manuscript. All authors reviewed the manuscript.

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Correspondence to Haozhen Situ.

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Liang, Y., Situ, H. & Zheng, ZJ. Polygamy relations for tripartite and multipartite quantum systems. Quantum Inf Process 23, 385 (2024). https://doi.org/10.1007/s11128-024-04597-2

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