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A family of monotone quantum relative entropies (1309.4046v1)
Published 16 Sep 2013 in math-ph, math.FA, and math.MP
Abstract: We study here the elementary properties of the relative entropy $\cH(A,B)=\tr[\phi(A)-\phi(B)-\phi'(B)(A-B)]$ for $\phi$ a convex function and $A,B$ bounded self-adjoint operators. In particular, we prove that this relative entropy is monotone if and only if $\phi'$ is operator monotone. We use this to appropriately define $\cH(A,B)$ in infinite dimension.
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