{
  "id": "1803.04913",
  "version": "v1",
  "published": "2018-03-13T16:15:37.000Z",
  "updated": "2018-03-13T16:15:37.000Z",
  "title": "On non-commutativity in quantum theory (I): from classical to quantum probability",
  "authors": [
    "Curcuraci Luca"
  ],
  "comment": "19 pages, 1 figure",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its consequences in the probabilistic description. Typically, a random phenomenon is described using the measure-theoretic formulation of probability theory. Such a description can also be done using algebraic methods, which are capable to deal with non-commutative random variables (like in quantum mechanics). Here we propose a method to construct a non-commutative probability theory starting from an ordinary measure-theoretic description of probability. This will be done using the entropic uncertainty relations between random variables, in order to evaluate the presence of non-commutativity in their algebraic description.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-13T16:15:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum theory",
      "quantum probability",
      "non-commutativity",
      "quantum mechanics",
      "ordinary measure-theoretic description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}