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

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.