Superactivation of monogamy relations for nonadditive quantum correlation measures
Zhi‐Xiang Jin, Shao-Ming Fei · Physical Review A · 2019
We investigate the general monogamy and polygamy relations satisfied by quantum correlation measures. We show that there exist two real numbers $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ such that for any quantum correlation measure $Q,{Q}^{x}$ is monogamous if $x\ensuremath{\ge}\ensuremath{\alpha}$ and polygamous if $0\ensuremath{\le}x\ensuremath{\le}\ensuremath{\beta}$ for a given multipartite state $\ensuremath{\rho}$. For $\ensuremath{\beta}<x<\ensuremath{\alpha}$, we show that the monogamy relation can be superactivated by finite $m$ copies ${\ensuremath{\rho}}^{\ensuremath{\bigotimes}m}$ of $\ensuremath{\rho}$ 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.