{
  "id": "1206.0630",
  "version": "v4",
  "published": "2012-06-04T14:23:53.000Z",
  "updated": "2013-05-08T18:22:06.000Z",
  "title": "Three-dimensionality of space and the quantum bit: an information-theoretic approach",
  "authors": [
    "Markus P. Mueller",
    "Lluis Masanes"
  ],
  "comment": "13 + 22 pages, 9 figures. v4: some clarifications, in particular in Section V / Appendix C (added Example 39)",
  "journal": "New J. Phys. 15, 053040 (2013)",
  "doi": "10.1088/1367-2630/15/5/053040",
  "categories": [
    "quant-ph",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "It is sometimes pointed out as a curiosity that the state space of quantum two-level systems, i.e. the qubit, and actual physical space are both three-dimensional and Euclidean. In this paper, we suggest an information-theoretic analysis of this relationship, by proving a particular mathematical result: suppose that physics takes place in d spatial dimensions, and that some events happen probabilistically (not assuming quantum theory in any way). Furthermore, suppose there are systems that carry \"minimal amounts of direction information\", interacting via some continuous reversible time evolution. We prove that this uniquely determines spatial dimension d=3 and quantum theory on two qubits (including entanglement and unitary time evolution), and that it allows observers to infer local spatial geometry from probability measurements.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-05-08T18:22:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "information-theoretic approach",
      "quantum bit",
      "infer local spatial geometry",
      "quantum theory",
      "three-dimensionality"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "New Journal of Physics",
      "year": 2013,
      "month": "May",
      "volume": 15,
      "number": 5,
      "pages": "053040"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1117050,
      "adsabs": "2013NJPh...15e3040M"
    }
  }
}