Quantum Bayes' rule and Petz transpose map from the minimum change principle
read the original 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.
This paper has not been read by Pith yet.
Forward citations
Cited by 4 Pith papers
-
Generating quantum ensembles via reverse-time quantum diffusions
The paper establishes a reverse-time quantum diffusion framework that generates complex quantum ensembles from simple distributions by deriving and learning a feedback Hamiltonian from forward trajectory data.
-
Exact large deviations and emergent long-range correlations in sequential quantum East circuits
Conditioning on rare boundary measurement outcomes in a quantum East circuit generates states with finite two-point correlations at arbitrary distances and an underlying Sierpiński-triangle fractal structure.
-
A quantum entropy production operator
Introduces a Hermitian entropy-production operator equal to Belavkin-Staszewski relative entropy that obeys exact fluctuation theorems for quantum forward-reverse pairs defined via Petz retrodiction.
-
Connecting Quantum Tomography and Quantum Retrodiction
The Petz recovery map equals the gradient of the log-likelihood in maximum-likelihood tomography, unifying retrodiction and state reconstruction via a shared iterative procedure.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.