Minimal sufficient Jordan algebras characterize sufficiency for positive trace-preserving maps on quantum states, with Neyman-Pearson tests generating them and equality in data-processing inequalities implying Petz recovery.
Quasi-Entropies for States of a von Neumann Algebra
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Quantum f-divergence equals classical f-divergence of Nussbaum-Szkoła distributions for normal states on semifinite von Neumann algebras.
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Sufficiency and Petz recovery for positive maps
Minimal sufficient Jordan algebras characterize sufficiency for positive trace-preserving maps on quantum states, with Neyman-Pearson tests generating them and equality in data-processing inequalities implying Petz recovery.
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Quantum $f$-divergences via Nussbaum-Szko{\l}a Distributions in Semifinite von Neumann Algebras
Quantum f-divergence equals classical f-divergence of Nussbaum-Szkoła distributions for normal states on semifinite von Neumann algebras.