{
  "id": "1104.2760",
  "version": "v1",
  "published": "2011-04-14T13:45:19.000Z",
  "updated": "2011-04-14T13:45:19.000Z",
  "title": "Numerical shadow and geometry of quantum states",
  "authors": [
    "Charles F. Dunkl",
    "Piotr Gawron",
    "John A. Holbrook",
    "Jarosław A. Miszczak",
    "Zbigniew Puchała",
    "Karol Życzkowski"
  ],
  "comment": "19 pages, 5 figures",
  "journal": "J. Phys. A: Math. Theor. 44, 335301 (2011)",
  "doi": "10.1088/1751-8113/44/33/335301",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP",
    "math.OA"
  ],
  "abstract": "The totality of normalised density matrices of order N forms a convex set Q_N in R^(N^2-1). Working with the flat geometry induced by the Hilbert-Schmidt distance we consider images of orthogonal projections of Q_N onto a two-plane and show that they are similar to the numerical ranges of matrices of order N. For a matrix A of a order N one defines its numerical shadow as a probability distribution supported on its numerical range W(A), induced by the unitarily invariant Fubini-Study measure on the complex projective manifold CP^(N-1). We define generalized, mixed-states shadows of A and demonstrate their usefulness to analyse the structure of the set of quantum states and unitary dynamics therein.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-14T13:45:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum states",
      "numerical shadow",
      "numerical range",
      "unitarily invariant fubini-study measure",
      "flat geometry"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2011,
      "month": "Aug",
      "volume": 44,
      "number": 33,
      "pages": 335301
    },
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011JPhA...44G5301D"
    }
  }
}