# Polygamy relations of multipartite entanglement beyond qubits

## TL;DR

This paper explores advanced polygamy inequalities for multipartite entanglement, providing tighter bounds and new relations for concurrence of assistance in high-dimensional quantum systems.

## Contribution

It introduces generalized polygamy inequalities for multipartite pure states and improves existing bounds under specific conditions.

## Key findings

- Derived $eta$th power polygamy inequalities tighter than previous ones.
- Provided lower bounds for bipartite entanglement distribution.
- Presented a detailed example illustrating the inequalities.

## Abstract

We investigate the polygamy relations related to the concurrence of assistance for any multipartite pure states. General polygamy inequalities given by the $\alpha$th $(0\leq \alpha\leq 2)$ power of concurrence of assistance is first presented for multipartite pure states in arbitrary-dimensional quantum systems. We further show that the general polygamy inequalities can even be improved to be tighter inequalities under certain conditions on the assisted entanglement of bipartite subsystems. Based on the improved polygamy relations, lower bound for distribution of bipartite entanglement is provided in a multipartite system. Moreover, the $\beta$th ($0\leq \beta \leq 1$) power of polygamy inequalities are obtained for the entanglement of assistance as a by-product, which are shown to be tighter than the existing ones. A detailed example is presented.