Schrödinger Bridges via the Hacking of Bayesian Priors in Classical and Quantum Regimes

Fuente: arXiv
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Main Authors: Aw, Clive Cenxin, Sidajaya, Peter
Format: Preprint
Published: 2026
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author Aw, Clive Cenxin
Sidajaya, Peter
author_facet Aw, Clive Cenxin
Sidajaya, Peter
contents Bayes' rule is widely regarded as the canonical prescription for belief updating. We show, however, that one can arbitrarily preserve pre-specified beliefs while appearing to perform Bayesian updates via "prior hacking": engineering a reference prior distribution such that, for a fixed channel and evidence, the update matches a chosen target distribution. We prove that this is generically possible in both classical and quantum settings whenever Bayesian inversions are well-defined (with the Petz recovery map as the quantum analogue to Bayes' rule), and provide constructive algorithms for doing so. We further establish a duality between prior hacking and Schrödinger bridge problems (a key object in statistical physics with applications in generative modelling), yielding in the quantum setting a unique, inference-consistent selection among candidate bridges. This formally establishes the Bayes-like updating that Schrödinger bridges are performing with respect to the process as opposed to the reference prior, both in classical and quantum settings.
format Preprint
id arxiv_https___arxiv_org_abs_2603_18665
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Schrödinger Bridges via the Hacking of Bayesian Priors in Classical and Quantum Regimes
Aw, Clive Cenxin
Sidajaya, Peter
Quantum Physics
Statistical Mechanics
Mathematical Physics
Bayes' rule is widely regarded as the canonical prescription for belief updating. We show, however, that one can arbitrarily preserve pre-specified beliefs while appearing to perform Bayesian updates via "prior hacking": engineering a reference prior distribution such that, for a fixed channel and evidence, the update matches a chosen target distribution. We prove that this is generically possible in both classical and quantum settings whenever Bayesian inversions are well-defined (with the Petz recovery map as the quantum analogue to Bayes' rule), and provide constructive algorithms for doing so. We further establish a duality between prior hacking and Schrödinger bridge problems (a key object in statistical physics with applications in generative modelling), yielding in the quantum setting a unique, inference-consistent selection among candidate bridges. This formally establishes the Bayes-like updating that Schrödinger bridges are performing with respect to the process as opposed to the reference prior, both in classical and quantum settings.
title Schrödinger Bridges via the Hacking of Bayesian Priors in Classical and Quantum Regimes
topic Quantum Physics
Statistical Mechanics
Mathematical Physics
url https://arxiv.org/abs/2603.18665