# Polygamy relation for the R\'enyi-$\alpha$ entanglement of assistance in multi-qubit systems

## TL;DR

This paper establishes a new polygamy relation for multi-qubit quantum entanglement using Rényi-$\alpha$ entanglement of assistance, generalizing previous inequalities and applicable within specific parameter ranges.

## Contribution

It introduces a novel polygamy inequality based on Rényi-$\alpha$ entanglement of assistance for multi-qubit systems, extending existing entanglement inequalities.

## Key findings

- Proves a new polygamy relation for Rényi-$\alpha$ entanglement of assistance.
- Shows the inequality holds for the $\mu$th power of the entanglement measure.
- Reduces to known inequalities when $\alpha$ is in a specific range.

## Abstract

We prove a new polygamy relation of multi-party quantum entanglement in terms of R\'{e}nyi-$\alpha$ entanglement of assistance for $\left( {\sqrt 7 - 1} \right)/2\leq\alpha \leq \left( {\sqrt 13 - 1} \right)/2$. This class of polygamy inequality reduces to the polygamy inequality based on entanglement of assistance since R\'{e}nyi-$\alpha$ entanglement is a generalization of entanglement of formation. We further show that the polygamy inequality also holds for the $\mu$th power of R\'{e}nyi-$\alpha$ entanglement of assistance.