{
  "id": "2112.03362",
  "version": "v2",
  "published": "2021-12-06T21:22:56.000Z",
  "updated": "2021-12-20T17:21:31.000Z",
  "title": "An approach to $p$-adic qubits from irreducible representations of $SO(3)_p$",
  "authors": [
    "Ilaria Svampa",
    "Stefano Mancini",
    "Andreas Winter"
  ],
  "comment": "42 pages",
  "journal": "J. Math. Phys. 63, 072202 (2022)",
  "doi": "10.1063/5.0089077",
  "categories": [
    "math-ph",
    "math.MP",
    "math.NT",
    "quant-ph"
  ],
  "abstract": "We introduce the notion of $p$-adic quantum bit ($p$-qubit) in the context of the $p$-adic quantum mechanics initiated and developed by Volovich and his followers. In this approach, physics takes place in three-dimensional $p$-adic space rather than Euclidean space. Based on our prior work describing the $p$-adic special orthogonal group, we outline a programme to classify its continuous unitary projective representations, which can be interpreted as a theory of $p$-adic angular momentum. The $p$-adic quantum bit arises from the irreducible representations of minimal nontrivial dimension two, of which we construct examples for all primes $p$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2021-12-20T17:21:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "irreducible representations",
      "adic qubits",
      "adic quantum bit arises",
      "adic special orthogonal group",
      "adic quantum mechanics"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "J. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}