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.
Positive linear maps of operator algebras
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Periodic properties of quantum channel sequences from ergodic processes are related to global spectral data via a Perron-Frobenius-type theorem.
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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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Periodicity in Ergodic Quantum Processes
Periodic properties of quantum channel sequences from ergodic processes are related to global spectral data via a Perron-Frobenius-type theorem.