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

TL;DR

This paper establishes new, tighter monogamy and polygamy inequalities for multi-qudit generalized W-class states using concurrence of assistance and Tsallis-$q$ entanglement of assistance, applicable even when CKW inequality fails.

Contribution

It introduces novel analytical monogamy inequalities for multi-qudit states based on assistance entanglement measures, extending validity beyond CKW inequality limits.

Findings

Derived tighter monogamy inequalities for generalized W-class states.

Established new monogamy and polygamy relations using Tsallis-$q$ entanglement of assistance.

Validated inequalities through detailed examples showing improvements over previous results.

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.