{
  "id": "2406.03775",
  "version": "v1",
  "published": "2024-06-06T06:26:49.000Z",
  "updated": "2024-06-06T06:26:49.000Z",
  "title": "Nonstandard derivation of the Gorini-Kossakowski-Sudarshan-Lindblad master equation of a quantum dynamical semigroup from the Kraus representation",
  "authors": [
    "Yui Kuramochi"
  ],
  "comment": "16 pages",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We give a new nonstandard proof of a well-known theorem that the generator $L$ of a quantum dynamical semigroup $\\exp(tL)$ on a finite-dimensional quantum system has a specific form called a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) generator (also known as a Lindbladian) and vice versa. The proof starts from the Kraus representation of the quantum channel $\\exp (\\delta t L)$ for an infinitesimal hyperreal number $\\delta t>0$ and then estimates the orders of the traceless components of the Kraus operators. The jump operators then naturally arise as the standard parts of the traceless parts divided by $\\sqrt{\\delta t}$. We also give a nonstandard proof of a related fact that close completely positive maps have close Kraus operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-06T06:26:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum dynamical semigroup",
      "gorini-kossakowski-sudarshan-lindblad master equation",
      "kraus representation",
      "nonstandard derivation",
      "nonstandard proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}