Superactivation of monogamy relations for nonadditive quantum correlation measures

Abstract

We investigate the general monogamy and polygamy relations satisfied by quantum correlation measures. We show that there exist two real numbers $\alpha$ and $\beta$ such that for any quantum correlation measure $Q$, $Q^x$ is monogamous if $x\geq \alpha$ and polygamous if $0\leq x\leq \beta$ for a given multipartite state $\rho$. For $\beta <x<\alpha$, we show that the monogamy relation can be superactivated by finite $m$ copies $\rho^{\otimes m}$ of $\rho$ for nonadditive correlation measures. As a detailed example, we use the negativity as the quantum correlation measure to illustrate such superactivation of monogamy properties. A tighter monogamy relation is presented at last.