Polygamy relation for the Rényi-$\hat{I}\pm$ entanglement of assistance in multi-qubit systems

Abstract

We prove a new polygamy relation of multi-party quantum entanglement in terms of Rényi-$\hat{I}\pm$ entanglement of assistance for $\left(\sqrt{7}-1\right)/2\le \hat{I}\pm \le \left(\sqrt{1}3-1\right)/2$. This class of polygamy inequality reduces to the polygamy inequality based on entanglement of assistance since Rényi-$\hat{I}\pm$ entanglement is a generalization of entanglement of formation. We further show that the polygamy inequality also holds for the $\hat{I}¼$th power of Rényi-$\hat{I}\pm$ entanglement of assistance.

6 pages, 7 figures