Superactivation of monogamy relations for nonadditive quantum correlation measures

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 >= alpha and polygamous if 0 <= x <= 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(circle times 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.