  We revisit the upper bound of quantum discord given by the von Neumann
entropy of the measured subsystem. Using the Koashi-Winter relation, we obtain
a trade-off between the amount of classical correlation and quantum discord in
the tripartite pure states. The difference between the quantum discord and its
upper bound is interpreted as a measure on the classical correlative capacity.
Further, we give the explicit characterization of the quantum states saturating
the upper bound of quantum discord, through the equality condition for the
Araki-Lieb inequality. We also demonstrate that the saturating of the upper
bound of quantum discord precludes any further correlation between the measured
subsystem and the environment.
