{
  "id": "quant-ph/0005132",
  "version": "v2",
  "published": "2000-05-31T21:49:02.000Z",
  "updated": "2000-08-29T17:29:12.000Z",
  "title": "On Quantum Detection and the Square-Root Measurement",
  "authors": [
    "Yonina C. Eldar",
    "G. David Forney Jr"
  ],
  "comment": "Version of August 29, 2000, with minor revisions. To appear in the IEEE Transactions on Information Theory. RevTex, 48 pages, 3 figures. A briefer version of this paper has also been submitted to Physical Review Letters. A copy is obtainable by writing to the authors at yonina@mit.edu",
  "journal": "IEEE Trans. Inform. Theory, vol. 47, pp. 858-872, Mar. 2001",
  "categories": [
    "quant-ph"
  ],
  "abstract": "In this paper we consider the problem of constructing measurements optimized to distinguish between a collection of possibly non-orthogonal quantum states. We consider a collection of pure states and seek a positive operator-valued measure (POVM) consisting of rank-one operators with measurement vectors closest in squared norm to the given states. We compare our results to previous measurements suggested by Peres and Wootters [Phys. Rev. Lett. 66, 1119 (1991)] and Hausladen et al. [Phys. Rev. A 54, 1869 (1996)], where we refer to the latter as the square-root measurement (SRM). We obtain a new characterization of the SRM, and prove that it is optimal in a least-squares sense. In addition, we show that for a geometrically uniform state set the SRM minimizes the probability of a detection error. This generalizes a similar result of Ban et al. [Int. J. Theor. Phys. 36, 1269 (1997)].",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-08-29T17:29:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "square-root measurement",
      "quantum detection",
      "measurement vectors closest",
      "possibly non-orthogonal quantum states",
      "geometrically uniform state set"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "RevTeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000quant.ph..5132E"
    }
  }
}