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. 
Lin Zhang and Junde Wu and Shao-Ming Fei
quant-ph math-ph math.MP