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.
Sufficient subalgebras and the relative entropy of states of a von neumann algebra
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VarQEC uses a distinguishability loss as a machine-learning objective to variationally discover resource-efficient encoding circuits optimized for given noise models.
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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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Learning Encodings by Maximizing State Distinguishability: Variational Quantum Error Correction
VarQEC uses a distinguishability loss as a machine-learning objective to variationally discover resource-efficient encoding circuits optimized for given noise models.