  Using the relative entropy of total correlation, we derive an expression
relating the mutual information of $n$-partite pure states to the sum of the
mutual informations and entropies of its marginals and analyze some of its
implications. Besides, by utilizing the extended strong subadditivity of von
Neumann entropy, we obtain generalized monogamy relations for the total
correlation in three-partite mixed states. These inequalities lead to a tight
lower bound for this correlation in terms of the sum of the bipartite mutual
informations. We use this bound to propose a measure for residual three-partite
total correlation and discuss the non-applicability of this kind of quantifier
to measure genuine multiparty correlations.
