General monogamy relation of multi-qubit systems in terms of squared Rényi-$\alpha$ entanglement

Abstract

We prove that the squared Rényi-$\alpha$ entanglement (SR$\alpha$E), which is the generalization of entanglement of formation (EOF), obeys a general monogamy inequality in an arbitrary $N$-qubit mixed state. Furthermore, for a class of Rényi-$\alpha$ entanglement, we prove that the monogamy relations of the SR$\alpha$E have a hierarchical structure when the $N$-qubit system is divided into $k$ parties. As a byproduct, the analytical relation between the Rényi-$\alpha$ entanglement and the squared concurrence is derived for bipartite $2\otimes d$ systems. Based on the monogamy properties of SR$\alpha$E, we can construct the corresponding multipartite entanglement indicators which still work well even when the indicators based on the squared concurrence and EOF lose their efficacy. In addition, the monogamy property of the $\mu$-th power of Rényi-$\alpha$ entanglement is analyzed.

8 pages, 5 figures, any comments are welcome

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