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arXiv · 2502.11526

Monogamy and polygamy for multi-qudit generalized $W$-class states based on concurrence of assistance and Tsallis-$q$ entanglement of assistance

Wen Zhou·Zhong-Xi Shen·Dong-Ping Xuan·Zhi-Xi Wang·Shao-Ming Fei
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Abstract

By analyzing the reduced density matrices derived from a generalized $W$-class state under any partition, we present new analytical monogamy inequalities satisfied by the $\alpha$-th ($\alpha\geq\gamma,~\gamma\geq2$) power and $\beta$-th ($0\leq\beta\leq\frac{\gamma}{2},~\gamma\geq2$) power of the concurrence of assistance for multi-qudit generalized $W$-class states, which are demonstrated to be tighter than previous studies through detailed examples. Furthermore, using the Tsallis-$q$ entanglement of assistance, we also establish new monogamy and polygamy relations, which are shown to be valid even for multipartite higher-dimensional states that the CKW inequality is violated.

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Wen Zhou, Zhong-Xi Shen, Dong-Ping Xuan, Zhi-Xi Wang, Shao-Ming Fei. 2025-02-17. Monogamy and polygamy for multi-qudit generalized $W$-class states based on concurrence of assistance and Tsallis-$q$ entanglement of assistance. https://doi.org/10.1140/epjp/s13360-025-06035-3

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