The f_0-divergence defined via Jordan decomposition integrals coincides with Araki's relative entropy on arbitrary von Neumann algebras, extending Frenkel's finite-dimensional formula.
Quantum $f$-divergences in von Neumann algebras I. Standard $f$-divergences
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abstract
We make a systematic study of standard $f$-divergences in general von Neumann algebras. An important ingredient of our study is to extend Kosaki's variational expression of the relative entropy to an arbitary standard $f$-divergence, from which most of the important properties of standard $f$-divergences follow immediately. In a similar manner we give a comprehensive exposition on the R\'enyi divergence in von Neumann algebra. Some results on relative hamiltonians formerly studied by Araki and Donald are improved as a by-product.
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Relative entropy of vacuum vs coherent state for λφ⁴ in the Rindler wedge equals the classical interacting boost charge to O(λ) and obeys the Bekenstein bound.
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Integral representations of $f$-divergences for general von Neumann algebras
The f_0-divergence defined via Jordan decomposition integrals coincides with Araki's relative entropy on arbitrary von Neumann algebras, extending Frenkel's finite-dimensional formula.
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Relative entropy for $\lambda \phi^4$ in the Rindler wedge
Relative entropy of vacuum vs coherent state for λφ⁴ in the Rindler wedge equals the classical interacting boost charge to O(λ) and obeys the Bekenstein bound.