A Bayesian Analogue of Gleason's Theorem
Quantum Physics
2015-06-26 v3
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.
Cite
@article{arxiv.quant-ph/0603065,
title = {A Bayesian Analogue of Gleason's Theorem},
author = {Thomas Marlow},
journal= {arXiv preprint arXiv:quant-ph/0603065},
year = {2015}
}
Comments
14 pages, v2: minor stylistic changes, v3: changes made in-line with to-be-published version