{
  "annotation_id": "5a5e37ae-3014-4b6b-8a8e-9db5cca5053c",
  "date_created": "2026-03-02T18:01:42.422000Z",
  "date_modified": "2026-03-02T18:01:42.422000Z",
  "file_hash": "9edc51c658c03330e236fb8b30ff943aab7d2e51e1782e91ea6036be27a93df7",
  "private": false,
  "record": {
    "abstract": "We give a useful new characterization of the set of all completely positive,\ntrace-preserving (i.e., stochastic) maps from 2x2 matrices to 2x2 matrices.\nThese conditions allow one to easily check any trace-preserving map for\ncomplete positivity. We also determine explicitly all extreme points of this\nset, and give a useful parameterization after reduction to a certain canonical\nform. This allows a detailed examination of an important class of non-unital\nextreme points which can be characterized as having exactly two images on the\nBloch sphere.\n  We also discuss a number of related issues about the images and the geometry\nof the set of stochastic maps, and show that any stochastic map on 2x2 matrices\ncan be written as a convex combination of two \"generalized\" extreme points.",
    "arxiv_id": "quant-ph/0101003",
    "authors": [
      "Mary Beth Ruskai",
      "Stanislaw Szarek",
      "Elisabeth Werner"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP",
      "math.OA",
      "math.RA"
    ],
    "journal_ref": "Lin. Alg. Appl. 347, 159--187 (2002)",
    "title": "An Analysis of Completely-Positive Trace-Preserving Maps on 2x2 Matrices",
    "url": "https://arxiv.org/abs/quant-ph/0101003"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "479bcf26-e12f-4e32-a5f0-4efdb62325a3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}