Unification of multi-qubit polygamy inequalities

TL;DR

This paper introduces a unified framework for understanding multi-qubit entanglement polygamy inequalities, generalizing existing inequalities and providing tighter bounds for three-qubit systems.

Contribution

It proposes a two-parameter generalization of entanglement of assistance and unifies various polygamy inequalities under this framework.

Findings

Established a broad class of polygamy inequalities for multi-qubit entanglement.

Provided an analytic lower bound for bipartite quantum states.

Improved inequalities specifically for three-qubit systems.

Abstract

We establish a unified view of polygamy of multi-qubit entanglement. We first introduce a two-parameter generalization of entanglement of assistance namely unified entanglement of assistance for bipartite quantum states, and provide an analytic lowerbound in two-qubit systems. We show a broad class of polygamy inequalities of multi-qubit entanglement in terms of unified entanglement of assistance that encapsulates all known multi-qubit polygamy inequalities as special cases. We further show that this class of polygamy inequalities can be improved into tighter inequalities for three-qubit systems.