A family of monotone quantum relative entropies

Abstract

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

References in corpus (2)

• The Hartree equation for infinitely many particles. I. Well-posedness theory
• A Nonlinear Model for Relativistic Electrons at Positive Temperature

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