  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.

Quantum Physics