Monogamy and Polygamy Relations of Quantum Correlations for Multipartite Systems

Abstract

We study the monogamy and polygamy inequalities of quantum correlations in arbitrary dimensional multipartite quantum systems. We first derive the monogamy inequality of the $\alpha$th ($0\leq\alpha\leq\frac{r}{2}, r\geq2$) power of concurrence for any $2\otimes2\otimes2^{n-2}$ tripartite states and generalize it to the $n$-qubit quantum states. In addition to concurrence, we show that the monogamy relations are satisfied by other quantum correlation measures such as entanglement of formation. Moreover, the polygamy inequality of the $\beta$th ($\beta\leq0$) power of concurrence and the $\beta$th ($\beta\geq s, 0\leq s\leq1$) power of the negativity are presented for $2\otimes2\otimes2^{n-2}$. We then obtain the polygamy inequalities of quantum correlations for multipartite states. Finally, our results are shown to be tighter than previous studies using detailed examples.