Breakthroughs of the Year: 2025

Bayes’ rule updates beliefs from new evidence and can be derived from a “minimum change” principle that alters prior beliefs only as much as necessary. Extending this idea to quantum states is challenging due to non-commutativity, and past proposals relied largely on formal analogies. This work derives a quantum Bayes’ rule directly from the minimum change principle, which often coincides with the Petz Transpose Map. However, when new evidence does not commute with expected evidence, it yields a previously unknown update map, indicating that quantum inference remains not fully understood.

Citation: Phys. Rev. Lett. 135, 090203 (2025)

Authors: G. Bai, F. Buscemi, V. Scarani