Monogamy and polygamy relations of quantum correlations for multipartite systems

TL;DR

This paper investigates monogamy and polygamy inequalities of quantum correlations in multipartite systems, deriving new bounds for concurrence, entanglement of formation, and negativity, which are shown to be tighter than previous results.

Contribution

It introduces generalized monogamy and polygamy inequalities for various quantum correlation measures in multipartite systems, extending and tightening existing bounds.

Findings

Derived monogamy inequality for the $ ext{α}$th power of concurrence in tripartite states.

Established polygamy inequalities for concurrence and negativity in multipartite states.

Showed that the new inequalities are tighter than previous bounds through examples.

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.