A family of monotone quantum relative entropies

We study here the elementary properties of the relative entropy $\cH(A,B)=\tr[ϕ(A)-ϕ(B)-ϕ'(B)(A-B)]$ for $ϕ$ a convex function and $A,B$ bounded self-adjoint operators. In particular, we prove that this relative entropy is monotone if and only if $ϕ'$ is operator monotone. We use this to appropriately define $\cH(A,B)$ in infinite dimension.

No reviews yet.

No comments yet.