Bayesian updating is supposed to be belief revision: you start with a prior, observe evidence, and the posterior reflects what you've learned. The prior encodes what you believed before; the evidence updates it. The process is honest — or so the framework implies.
This paper shows you can hack the prior. Given any fixed channel (likelihood) and evidence, there exists a prior distribution such that the Bayesian update produces any desired posterior. The posterior is chosen first; the prior is reverse-engineered to produce it. The update is formally correct — Bayes' theorem is satisfied — but the conclusion was predetermined.
The construction is not merely a curiosity. The authors prove a duality between prior hacking and Schrödinger bridge problems from statistical physics. Schrödinger bridges find the most likely process connecting two endpoint distributions; prior hacking finds the starting distribution that makes a given endpoint inevitable under Bayesian updating. The two problems are the same problem in dual form.
In the quantum setting (using the Petz recovery map as quantum Bayes' rule), the duality becomes cleaner: the quantum constraint uniquely selects among candidate bridges, resolving an ambiguity that persists classically. Quantum mechanics narrows the solution space. The richer structure restricts rather than enables — and the restriction produces a unique, well-defined answer where the classical theory leaves a family.