Polygamy relation for the Rényi-$\alpha$ entanglement of assistance in multi-qubit systems

Abstract

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

arXiv comment6 pages, 7 figures

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• Monogamy of quantum entanglement
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• Tighter monogamy and polygamy relations of quantum entanglement in multi-qubit systems