MathDBCategorical characterization of the Petz recovery map
Categorical characterization of the Petz recovery map
Let be a retrodiction, or quantum Bayesian inversion, assignment for normal quantum processes between von Neumann algebras equipped with faithful states, satisfying the proposed categorical axioms for retrodiction. Is necessarily equal, for every such process and faithful state, to the corresponding Petz recovery map ? Equivalently, do the categorical axioms uniquely characterize the Petz recovery map in the infinite-dimensional von Neumann-algebraic setting, so that ?
Progress summary
A new formulation sharpens the infinite-dimensional question but does not settle whether the Petz recovery map is uniquely characterized.
The problem asks whether a proposed structural description of quantum Bayesian inversion uniquely identifies the Petz recovery map in the infinite-dimensional setting. No proposer or original date is identified in the available record.
August 2026 formalization
The question has been formalized with a detailed framework for faithful states on von Neumann algebras, clarifying its mathematical scope. The source explicitly makes no claim to resolve the uniqueness question.
Current status (as of August 2026): The infinite-dimensional problem is more precisely formulated, but uniqueness of the categorical characterization remains open.
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