Tightening monogamy and polygamy relations of unified entanglement in multipartite systems

Abstract: We study the monogamy and polygamy inequalities of unified entanglement in multipartite quantum systems. We first derive the monogamy inequality of unified-$(q, s)$ entanglement for multi-qubit states under arbitrary bipartition, and then obtain the monogamy inequalities of the $\alpha$th ($0\leq\alpha\leq\frac{r}{2}, r\geq\sqrt{2}$) power of entanglement of formation for tripartite states and their generalizations in multi-qubit quantum states. We also generalize the polygamy inequalities of unified-$(q, s)$ entanglement for multi-qubit states under arbitrary bipartition. Moreover, we investigate polygamy inequalities of the $\beta$th ($\beta\geq \max{1, s}, 0\leq s\leq s_0, 0\leq s_0\leq\sqrt{2}$) power of the entanglement of formation for $2\otimes2\otimes2$ and $n$-qubit quantum systems. Finally, using detailed examples, we show that the results are tighter than previous studies.