Note on a Family of Monotone Quantum Relative Entropies

@article{Deuchert2015NoteOA,
  title={Note on a Family of Monotone Quantum Relative Entropies},
  author={A. Deuchert and C. Hainzl and R. Seiringer},
  journal={Letters in Mathematical Physics},
  year={2015},
  volume={105},
  pages={1449-1466}
}
Given a convex function $${\varphi}$$φ and two hermitian matrices A and B, Lewin and Sabin study in (Lett Math Phys 104:691–705, 2014) the relative entropy defined by $${\mathcal{H}(A,B)={\rm Tr} \left[ \varphi(A) - \varphi(B) - \varphi'(B)(A-B) \right]}$$H(A,B)=Trφ(A)-φ(B)-φ′(B)(A-B). Among other things, they prove that the so-defined quantity is monotone if and only if $${\varphi'}$$φ′ is operator monotone. The monotonicity is then used to properly define $${\mathcal{H}(A,B)}$$H(A,B) for… Expand
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A Family of Monotone Quantum Relative Entropies
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