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Tighter constraints of multiqubit entanglement for negativity

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Abstract

We provide a characterization of multiqubit entanglement monogamy and polygamy constraints in terms of negativity. Using the square of convex-roof extended negativity (SCREN) and the Hamming weight of the binary vector related to the distribution of subsystems proposed in Kim (Phys Rev A 97:012334, 2018), we provide a new class of monogamy inequalities of multiqubit entanglement based on the \(\alpha \)th power of SCREN for \(\alpha \ge 1\) and polygamy inequalities for \(0\le \alpha \le 1\) in terms of squared convex-roof extended negativity of assistance (SCRENoA). For the case \(\alpha <0\), we give the corresponding polygamy and monogamy relations for SCREN and SCRENoA, respectively. We also show that these new inequalities give rise to tighter constraints than the existing ones.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Nos. 11805143 and 11675113, and NSF of Beijing under No. KZ201810028042.

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Authors and Affiliations

  1. State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, 100084, China

    Long-Mei Yang

  2. School of Mathematical Sciences, Tianjin Normal University, Tianjin, 300387, China

    Bin Chen

  3. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Shao-Ming Fei & Zhi-Xi Wang

  4. Max-Planck-Institute for Mathematics in the Sciences, 04103, Leipzig, Germany

    Shao-Ming Fei

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  1. Long-Mei Yang
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  2. Bin Chen
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  3. Shao-Ming Fei
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  4. Zhi-Xi Wang
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Correspondence to Zhi-Xi Wang.

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Yang, LM., Chen, B., Fei, SM. et al. Tighter constraints of multiqubit entanglement for negativity. Quantum Inf Process 19, 4 (2020). https://doi.org/10.1007/s11128-019-2513-1

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