Complementary monogamy and polygamy properties among multipartite systems

Abstract

Abstract Monogamy and polygamy relations are essential properties of quantum entanglement, which characterize the distributions of entanglement in multipartite systems. In this paper, we establish the general monogamy relations for $\gamma$th $(0\leq\gamma \leq\alpha, \alpha\geq 1)$ power of quantum entanglement based on unified-$(q,s)$ entanglement and polygamy relations for $\delta$th $(\delta\geq \beta, 0\leq\beta\leq1)$ power of entanglement of assistance based on unified-$(q,s)$ entanglement of assistance, which provides a complement to the previous research in terms of different parameter regions of $\gamma$ and $\delta$. These results are then applied to specific quantum correlations, e.g. entanglement of formation, Renyi-$q$ entanglement of assistance and Tsallis-$q$ entanglement of assistance to get the corresponding monogamy and polygamy inequalities. Moreover, typical examples are presented for illustration.