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Quantum Bayes' Rule and Petz Transpose Map from the Minimum Change Principle.

Ge Bai^1,2, Francesco Buscemi³, Valerio Scarani^1,4

¹National University of Singapore, Centre for Quantum Technologies, 3 Science Drive 2, Singapore 117543.

Physical Review Letters

|September 15, 2025

Summary

This summary is machine-generated.

We introduce a quantum Bayes' rule derived from a minimum change principle. This quantum rule updates beliefs using new evidence while minimally altering prior quantum information, analogous to classical Bayes' rule.

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Area of Science:

Quantum Information Theory
Foundations of Probability

Background:

Bayes' rule updates beliefs with new evidence, derived from a minimum change principle.
Classical Bayes' rule minimizes changes between joint input-output distributions and their marginals.

Purpose of the Study:

Introduce a quantum analog of the minimum change principle.
Derive a quantum Bayes' rule by minimizing changes between quantum input-output processes.

Main Methods:

Formulated a quantum minimum change principle.
Minimized the change between quantum input-output processes, not just their marginals.
Maximized fidelity for a unique solution.

Main Results:

Derived a quantum Bayes' rule based on the quantum minimum change principle.
The quantum Bayes' rule recovers the Petz transpose map under fidelity maximization.

Conclusions:

The quantum minimum change principle provides a novel foundation for quantum probability updating.
This work establishes a quantum analog to classical Bayesian inference with potential applications in quantum information processing.