{
  "id": "1907.11122",
  "version": "v1",
  "published": "2019-07-25T15:07:13.000Z",
  "updated": "2019-07-25T15:07:13.000Z",
  "title": "Canonical divergence for flat $α$-connections: Classical and Quantum",
  "authors": [
    "Domenico Felice",
    "Nihat Ay"
  ],
  "comment": "16 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "A recently introduced canonical divergence for a dualistic structure $(\\mathrm{g},\\nabla,\\nabla^*)$ on a smooth manifold $\\mathrm{M}$ is considered for flat $\\alpha$-connections. In the classical setting, we compute the recent canonical divergence on the manifold of positive measures and prove that it coincides with the classical $\\alpha$-divergence. In the quantum framework, such a divergence is evaluated for the quantum $\\alpha$-connections on the manifold of positive definite matrices. Also, in this case we obtain that the recent canonical divergence is the quantum $\\alpha$-divergence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-25T15:07:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "canonical divergence",
      "connections",
      "quantum framework",
      "dualistic structure",
      "smooth manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}