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arXiv · 2410.00319

Quantum Bayes' rule and Petz transpose map from the minimum change principle

Ge Bai·Francesco Buscemi·Valerio Scarani
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Abstract

Bayes' rule, which is routinely used to update beliefs based on new evidence, can be derived from a principle of minimum change. This principle states that updated beliefs must be consistent with new data, while deviating minimally from the prior belief. Here, we introduce a quantum analog of the minimum change principle and use it to derive a quantum Bayes' rule by minimizing the change between two quantum input-output processes, not just their marginals. This is analogous to the classical case, where Bayes' rule is obtained by minimizing several distances between the joint input-output distributions. When the change maximizes the fidelity, the quantum minimum change principle has a unique solution, and the resulting quantum Bayes' rule recovers the Petz transpose map in many cases.

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Ge Bai, Francesco Buscemi, Valerio Scarani. 2024-10-01. Quantum Bayes' rule and Petz transpose map from the minimum change principle. https://doi.org/10.1103/5n4p-bxhm

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