A Bayesian Analogue of Gleason's Theorem
arXiv:quant-ph/0603065 · doi:10.1063/1.2390658
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.
14 pages, v2: minor stylistic changes, v3: changes made in-line with to-be-published version
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