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Monogamy and Polygamy Relations of Quantum Correlations for Multipartite Systems

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Abstract

We study the monogamy and polygamy inequalities of quantum correlations in arbitrary dimensional multipartite quantum systems. We first derive the monogamy inequality of the α th \(\left (0\leq \alpha \leq \frac {r}{2}, r\geq 2\right )\) power of concurrence for any 2 ⊗ 2 ⊗ 2n− 2 tripartite states and generalize it to the n-qubit quantum states. In addition to concurrence, we show that the monogamy relations are satisfied by other quantum correlation measures such as entanglement of formation. Moreover, the polygamy inequality of the β th (β ≤ 0) power of concurrence and the β th (β ≥ s, 0 ≤ s ≤ 1) power of the negativity are presented for 2 ⊗ 2 ⊗ 2n− 2. We then obtain the polygamy inequalities of quantum correlations for multipartite states. Finally, our results are shown to be tighter than previous studies using detailed examples.

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Acknowledgements

This work is supported in part by the Simons Foundation under grant no. 523868 and the National Natural Science Foundation of China under grant nos. 12126351 and 12126314.

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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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  3. Hui Zhao
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Correspondence to Naihuan Jing.

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Zhang, MM., Jing, N. & Zhao, H. Monogamy and Polygamy Relations of Quantum Correlations for Multipartite Systems. Int J Theor Phys 61, 6 (2022). https://doi.org/10.1007/s10773-022-04971-9

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