General monogamy and polygamy relations of arbitrary quantum correlations for multipartite systems

Abstract: Monogamy and polygamy of quantum correlations are the fundamental properties of quantum systems. We study the monogamy and polygamy relations satisfied by any quantum correlations in multipartite quantum systems. General monogamy relations are presented for the $\alpha$th $(0\leq\alpha \leq\gamma$, $\gamma\geq2)$ power of quantum correlation, and general polygamy relations are given for the $\beta$th $(\beta\geq \delta$, $0\leq\delta\leq1)$ power of quantum correlation. We show that these newly derived monogamy and polygamy inequalities are tighter than the existing ones. By applying these results to specific quantum correlations such as concurrence and the square of convex-roof extended negativity of assistance (SCRENoA), the corresponding new classes of monogamy and polygamy relations are obtained, which include the existing ones as special cases. Detailed examples are given to illustrate the advantages of our results.