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

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 ($\alpha \ge \gamma ,\gamma \ge 2$) power and $\beta$-th ($0\le \beta \le \frac{\gamma }{2},\gamma \ge 2$) 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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