A Bayesian Analogue of Gleason's Theorem

Details A Bayesian Analogue of Gleason's Theorem A Bayesian Analogue of Gleason's Theorem

2006-03-08

arxiv.org/abs/quant-ph/0603065v3

Physics

Quantum Physics

14 pages, v2: minor stylistic changes, v3: changes made in-line with to-be-published version

Scientific paper

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.

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