Broader settings for retrodiction functors

Identify contexts beyond classical and quantum probability described by von Neumann algebras in which retrodiction functors appear, and determine whether the definition of a retrodiction functor is sufficiently robust to support development as an abstract categorical concept for specialization to diverse settings.

Background

The paper develops retrodiction functors categorically for von Neumann algebras and interprets the Petz retrodiction functor as a noncommutative extension of Bayesian inversion. The authors suggest that the same formalism may generalize time reversal or, categorically, inversion.

The unresolved question is whether retrodiction functors occur in settings outside the classical and quantum probability framework considered in the paper and whether the axiomatic definition is sufficiently robust for broad categorical use.

References

Beyond classical and quantum probability as described by von~Neumann algebras, in what other context do retrodiction functors appear? Is the definition sufficiently robust enough so as to merit being further developed as an abstract categorical concept to be later specialized in a variety of settings?

— Bayesian inference and retrodiction for faithful states on von Neumann algebras  (2608.20001 - Karmakar et al., 20 Aug 2026) in Item (5), Section 9, “Summary and discussion” (page number unavailable)