A family of monotone quantum relative entropies
arXiv:1309.4046 · doi:10.1007/s11005-014-0689-y
Abstract
We study here the elementary properties of the relative entropy $\cH(A,B)=\tr[Ï(A)-Ï(B)-Ï'(B)(A-B)]$ for $Ï$ a convex function and $A,B$ bounded self-adjoint operators. In particular, we prove that this relative entropy is monotone if and only if $Ï'$ is operator monotone. We use this to appropriately define $\cH(A,B)$ in infinite dimension.