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A Bayesian Analogue of Gleason's Theorem

Thomas Marlow
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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.

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Thomas Marlow. 2006-10-12. A Bayesian Analogue of Gleason's Theorem. https://doi.org/10.1063/1.2390658

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