{
  "id": "2403.06346",
  "version": "v1",
  "published": "2024-03-11T00:18:53.000Z",
  "updated": "2024-03-11T00:18:53.000Z",
  "title": "On the rational invariants of quantum systems of $n$-qubits",
  "authors": [
    "Luca Candelori",
    "Vladimir Y. Chernyak",
    "John R. Klein"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "math.QA",
    "math.RA",
    "math.RT",
    "quant-ph"
  ],
  "abstract": "For an $n$-qubit system, a rational function on the space of mixed states which is invariant with respect to the action of the group of local symmetries may be viewed as a detailed measure of entanglement. We show that the field of all such invariant rational functions is purely transcendental over the complex numbers and has transcendence degree $4^n - 2n-1$. An explicit transcendence basis is also exhibited.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-11T00:18:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81P40",
      "81P42",
      "13A50",
      "14L24"
    ],
    "keywords": [
      "quantum systems",
      "rational invariants",
      "invariant rational functions",
      "explicit transcendence basis",
      "complex numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}