Tighter monogamy and polygamy relations for a superposition of the generalized $W$-class state and vacuum

TL;DR

This paper derives tighter monogamy and polygamy inequalities for a superposition of generalized W-class states and vacuum, using Tsallis-$q$ and Rényi-$eta$ entanglement measures, enhancing understanding of entanglement distribution.

Contribution

It introduces new, tighter monogamy and polygamy relations for superposed states using Hamming weight and entanglement measures, improving upon previous inequalities.

Findings

Derived tighter monogamy inequalities using Tsallis-$q$ entanglement.

Established improved polygamy relations with Rényi-$eta$ entanglement.

Provided detailed examples illustrating entanglement distribution.

Abstract

Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We investigate the monogamy and polygamy relations with respect to any partitions for a superposition of the generalized $W$-class state and vacuum in terms of the Tsallis-$q$ entanglement and the R\'enyi-$\alpha$ entanglement. By using the Hamming weight of the binary vectors related to the partitions of the subsystems, new classes of monogamy and polygamy inequalities are derived, which are shown to be tighter than the existing ones. Detailed examples are presented to illustrate the finer characterization of entanglement distributions.