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Monogamy and polygamy for the generalized W-class states using unified-(q, s) entropy

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Abstract

We describe the entanglement distribution and restricted shareability of the multipartite generalized W-class states and their reduced density matrix under arbitrary partitions by using monogamy and polygamy relation based on the unified-(q, s) entropy. Firstly, we provide an analytical formula of unified-(q, s) entanglement (UE) and an analytical lower bound of unified-(q, s) entanglement of assistance (UEoA) for a reduced density matrix of a generalized W-class state. Then, we use these two analytical formulas to derive the monogamy and polygamy inequalities for a reduced density matrix of a qudit generalized W-class (GW) state. We establish two partition-dependent residual entanglements based on the new monogamy relation, which is helpful to obtain a comprehensive analysis of entanglement dynamics of generalized W-class states. Further, we investigate tighter monogamy and polygamy relations based on the power of αth (α ≥ 0) for UE and βth (β ≥ 0) for UEoA, respectively. The results show that the entanglement distribution characteristics of generalized W-class states satisfying stronger constraints can be described more accurately.

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Authors and Affiliations

  1. School of Computer and Computing Science, Hangzhou City University, Hangzhou, 310015, China

    Bo Li

  2. Department of Mathematics, East China University of Technology, Nanchang, 330013, China

    Bing Xie

  3. School of Information & Electronic Engineering (Sussex Artificial Intelligence Institute), Zhejiang Gongshang University, Hangzhou, 310018, China

    Zhanjun Zhang

  4. Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China

    Heng Fan

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  1. Bo Li
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  4. Heng Fan
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Correspondence to Zhanjun Zhang.

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Conflict of interest The authors declare that they have no conflict of interest.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12175147, 12075205, and T2121001), and Zhejiang Provincial Natural Science Foundation of China (Grant No. Z24A050006).

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Li, B., Xie, B., Zhang, Z. et al. Monogamy and polygamy for the generalized W-class states using unified-(q, s) entropy. Sci. China Phys. Mech. Astron. 67, 210312 (2024). https://doi.org/10.1007/s11433-023-2174-9

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