{
  "id": "quant-ph/0603065",
  "version": "v3",
  "published": "2006-03-08T12:17:48.000Z",
  "updated": "2006-10-12T10:29:23.000Z",
  "title": "A Bayesian Analogue of Gleason's Theorem",
  "authors": [
    "Thomas Marlow"
  ],
  "comment": "14 pages, v2: minor stylistic changes, v3: changes made in-line with to-be-published version",
  "categories": [
    "quant-ph"
  ],
  "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.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-10-12T10:29:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gleasons theorem",
      "bayesian analogue",
      "quantum history theories",
      "ad hoc mathematical axioms",
      "tentative novel axiom"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}