Weighted polygamy inequalities of multiparty entanglement in arbitrary dimensional quantum systems

TL;DR

This paper generalizes polygamy inequalities for multiparty entanglement in high-dimensional quantum systems using weighted measures and binary vector analysis, providing tighter bounds under certain conditions.

Contribution

It introduces a new class of weighted polygamy inequalities for multiparty entanglement applicable to arbitrary dimensions, improving existing bounds with additional conditions.

Findings

Established weighted polygamy inequalities using $eta$th-power of entanglement of assistance.

Showed inequalities can be tightened under specific conditions.

Applicable to arbitrary dimensional quantum systems.

Abstract

We provide a generalization for the polygamy constraint of multiparty entanglement in arbitrary dimensional quantum systems. By using the $\beta$th-power of entanglement of assistance for $0\leq \beta \leq1$ and the Hamming weight of the binary vector related with the distribution of subsystems, we establish a class of weighted polygamy inequalities of multiparty entanglement in arbitrary dimensional quantum systems. We further show that our class of weighted polygamy inequalities can even be improved to be tighter inequalities with some conditions on the assisted entanglement of bipartite subsystems.