Iterating & Hacking Bayes' Rule in both Classical & Quantum Regimes

Quantum versions of Bayesian updating should reproduce classical behaviour while respecting genuinely quantum transformations. This talk reviews existing proposals, then examines repeated-evidence limits and updating beliefs about transformations themselves. The Petz recovery map and Leifer–Spekkens conditional states supply these structures and connect the second kind of update to Schrödinger bridges in optimal transport.