1210.4720 (Lin Zhang et al.)

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

Lin Zhang, Shao-Ming Fei, Junde Wu

J. Rau derived in [Phys. Lett. A 374: 3715-3717 (2010).] a monotonicity property of relative entropy by Jaynes' argument for the second law as a motivation, that is, monotonicity of relative entropy under nonlinear coarse-graining. Based on this fact, he obtained the \emph{superadditivity inequality}---a much stronger monotonicity---of relative entropy: $$ \rS(\rho_{AB}||\sigma_{AB})\geqslant \rS(\rho_A||\sigma_A) + \rS(\rho_B||\sigma_B), $$ where $\rho_{AB}$ and $\sigma_{AB}$ are bipartite states on $\cH_A\ot\cH_B$. We provide a simple counterexample to show that the above inequality is not correct.

View original: http://arxiv.org/abs/1210.4720