A Bayesian Analogue of Gleason's Theorem

Abstract

We introduce a novel notion of probability within quantum history theories and give a Gleasonesque proof for these assignments. This involves introducing a tentative novel axiom of probability. We also discuss how we are to interpret these generalised probabilities as partially ordered notions of preference and we introduce a tentative generalised notion of Shannon entropy. A Bayesian approach to probability theory is adopted throughout, thus the axioms we use will be minimal criteria of rationality rather than ad hoc mathematical axioms.