Monogamy deficit for quantum correlations in a multipartite quantum system

We introduce the concept of monogamy deficit for quantum correlation by combining two types of monogamy inequalities depending on different measurement sides. For tripartite pure states, we demonstrate a relation which connects two types of monogamy inequalities for quantum discord and provide the difference between them. By using this relation, we obtain a unified physical interpretation for these two monogamy deficits. In addition, we find the interesting fact that there is a general monogamy condition for several quantum correlations for tripartite pure states. We then provide a necessary and sufficient condition for the establishment of one kind of monogamy inequality for tripartite mixed states and generalize it to multipartite quantum states.