  For a bipartite quantum system consisting of subsystems A and B it was shown
by Zhang et al. (Physics Letters A 376 (2012) 3588-3592) that the amount of
classical correlations, which is used to define the quantum discord, is known
to be bounded from above by the minimum of the von Neumann entropies of the
subsystems A and B. We provide an alternative proof that is shorter and more
transparent as it works without defining correlation matrices.
