Quantum Bayes’ Rule from the Principle of Minimal Change and Its Applications

Quantum Bayes’ Rule from the Principle of Minimal Change and Its Applications

Seminar author:Francesco Buscemi

Event date and time:03/19/2026 02:30:pm

Event location:GIQ Seminar Room

Event contact:

The principle of minimal change requires that an update incorporate new data while remaining as close as possible to the prior. In the classical setting, this requirement uniquely determines Bayes’ rule. In this talk, I present a quantum formulation of the same principle and derive its unique closed‑form solution, which can be regarded as a quantum version of Bayes’ rule. I discuss its connection with Petz’s transpose map and show how it can be applied to the retrodiction of quantum measurements. This retrodictive approach leads to new entropic uncertainty relations that are often stronger than existing ones and that also come with an intriguing operational interpretation. This work is based on:

1. G. Bai, F. Buscemi, and V. Scarani; PRL 135, 090203 (2025). https://arxiv.org/abs/2410.00319 
2. T. Nagasawa, E. Wakakuwa, K. Kato, and F. Buscemi; ROPP 88, 117601 (2025). https://arxiv.org/abs/2504.12738 
3. J. Kuang, K. Torii, and Francesco Buscemi: Quantum measurement retrodiction and entropic uncertainty relations. https://arxiv.org/abs/2511.20281