{
  "id": "quant-ph/0404137",
  "version": "v1",
  "published": "2004-04-23T19:02:29.000Z",
  "updated": "2004-04-23T19:02:29.000Z",
  "title": "Minimal Informationally Complete Measurements for Pure States",
  "authors": [
    "Steven T. Flammia",
    "Andrew Silberfarb",
    "Carlton M. Caves"
  ],
  "comment": "2 figures, submitted for the Asher Peres festschrift",
  "journal": "Foundations of Physics, Volume 35, Issue 12, Dec 2005, pp. 1985 - 2006",
  "doi": "10.1007/s10701-005-8658-z",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We consider measurements, described by a positive-operator-valued measure (POVM), whose outcome probabilities determine an arbitrary pure state of a D-dimensional quantum system. We call such a measurement a pure-state informationally complete (PSI-complete) POVM. We show that a measurement with 2D-1 outcomes cannot be PSI-complete, and then we construct a POVM with 2D outcomes that suffices, thus showing that a minimal PSI-complete POVM has 2D outcomes. We also consider PSI-complete POVMs that have only rank-one POVM elements and construct an example with 3D-2 outcomes, which is a generalization of the tetrahedral measurement for a qubit. The question of the minimal number of elements in a rank-one PSI-complete POVM is left open.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-04-23T19:02:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimal informationally complete measurements",
      "2d outcomes",
      "arbitrary pure state",
      "outcome probabilities determine",
      "d-dimensional quantum system"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Foundations of Physics",
      "year": 2005,
      "month": "Dec",
      "volume": 35,
      "number": 12,
      "pages": 1985
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005FoPh...35.1985F"
    }
  }
}