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In this Letter, two counterexamples show that the superadditivity inequalityof 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.

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