Optimal trace inequalities are derived for single-shot quantum information, replacing prior constants with a smaller Lambert-W prefactor for logarithmic traces and providing optimal two-sided collision-divergence bounds.
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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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Optimal Trace Inequalities for Single-Shot Quantum Information
Optimal trace inequalities are derived for single-shot quantum information, replacing prior constants with a smaller Lambert-W prefactor for logarithmic traces and providing optimal two-sided collision-divergence bounds.
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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.