Abstract
We consider both known and not previously studied trace functions with applications in quantum physics. By using perspectives we obtain convexity statements for different notions of residual entropy, including the entropy gain of a quantum channel studied by Holevo and others. We give new proofs of Carlen-Lieb’s concavity/convexity theorems for certain trace functions, by making use of the theory of operator monotone functions. We then apply these methods in a study of new classes of trace functions.
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