Comment on "Convergence of macrostates under reproducible processes" [Phys. Lett. A 374: 3715-3717 (2010)]

In this Letter, two counterexamples show that the superadditivity inequality of relative entropy is not true even for the full-ranked quantum states. Thus, an inequality of quantum channels and complementary channels is not also true. Finally, a conjecture of weak superadditivity inequality is presented.