Conditions for monogamy of quantum correlations in multipartite systems

• Monogamy of quantum correlations.
• Monogamous quantum correlation measures remain so on raising of power.
• Non-monogamous quantum correlations remain so on lowering of power.
• Monogamy of a convex quantum correlation measure for an arbitrary multipartite pure quantum state leads to its monogamy for the mixed states.
• A new monogamy inequality for quantum correlations, stronger than the standard one.

Monogamy of quantum correlations is a vibrant area of research because of its potential applications in several areas in quantum information ranging from quantum cryptography to co-operative phenomena in many-body physics. In this paper, we investigate conditions under which monogamy is preserved for functions of quantum correlation measures. We prove that a monogamous measure remains monogamous on raising its power, and a non-monogamous measure remains non-monogamous on lowering its power. We also prove that monogamy of a convex quantum correlation measure for arbitrary multipartite pure quantum state leads to its monogamy for mixed states in the same Hilbert space. Monogamy of squared negativity for mixed states and that of entanglement of formation follow as corollaries of our results.