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

May 25, 2026 PIRSA:26050067 Scientific Series Quantum Foundations

Aw, C. (2026). Iterating & Hacking Bayes' Rule in both Classical & Quantum Regimes. Perimeter Institute. https://pirsa.org/26050067

Aw, Clive. Iterating & Hacking Bayes' Rule in both Classical & Quantum Regimes. Perimeter Institute, May. 25, 2026, https://pirsa.org/26050067

@misc{ pirsa_PIRSA:26050067,
  doi = {10.48660/26050067},
  url = {https://pirsa.org/26050067},
  author = {Aw, Clive},
  keywords = {Quantum Foundations},
  language = {en},
  title = {Iterating \& Hacking Bayes{\textquoteright} Rule in both Classical \& Quantum Regimes},
  publisher = {Perimeter Institute},
  year = {2026},
  month = {may},
  note = {PIRSA:26050067 see, \url{https://pirsa.org}}
}

Abstract

Recent work on identifying a canonical analogue of Bayes’ rule in the quantum regime has produced a variety of proposals that both recover classical Bayesian features and highlight genuinely quantum aspects of state updating under physical transformations. In this talk, we briefly review the main approaches and key results in this programme.

We then focus on two additional structural features that viable quantum analogues to Bayes’ rule should satisfy. First, iterated Bayesian updating under repeated evidence should exhibit asymptotic “frequentist” behaviour, in the sense that the influence of the prior washes out. Second, there should exist a dual notion of updating not only beliefs about states, but also about the transformations themselves—an operation that naturally connects Bayesian inference with optimal transport objects known as Schrödinger bridges.

We argue that both features are realised within the framework of the Petz recovery map and the corresponding update rule arising from the Leifer–Spekkens conditional state formalism.