{
  "id": "1001.2029",
  "version": "v1",
  "published": "2010-01-12T21:41:14.000Z",
  "updated": "2010-01-12T21:41:14.000Z",
  "title": "Hedged maximum likelihood estimation",
  "authors": [
    "Robin Blume-Kohout"
  ],
  "comment": "4 pages + 2 short appendices",
  "journal": "Phys. Rev. Lett. 105, 200504 (2010)",
  "doi": "10.1103/PhysRevLett.105.200504",
  "categories": [
    "quant-ph"
  ],
  "abstract": "This paper proposes and analyzes a new method for quantum state estimation, called hedged maximum likelihood (HMLE). HMLE is a quantum version of Lidstone's Law, also known as the \"add beta\" rule. A straightforward modification of maximum likelihood estimation (MLE), it can be used as a plugin replacement for MLE. The HMLE estimate is a strictly positive density matrix, slightly less likely than the ML estimate, but with much better behavior for predictive tasks. Single-qubit numerics indicate that HMLE beats MLE, according to several metrics, for nearly all \"true\" states. For nearly-pure states, MLE does slightly better, but neither method is optimal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-12T21:41:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.67.-a",
      "03.65.Wj",
      "42.50.Dv"
    ],
    "keywords": [
      "hedged maximum likelihood estimation",
      "quantum state estimation",
      "hmle beats mle",
      "quantum version",
      "add beta"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review Letters",
      "year": 2010,
      "month": "Nov",
      "volume": 105,
      "number": 20,
      "pages": 200504
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010PhRvL.105t0504B"
    }
  }
}