{
  "annotation_id": "fb3b944e-7b8d-4300-8226-3bfb3102de74",
  "date_created": "2026-03-02T18:02:34.530000Z",
  "date_modified": "2026-03-02T18:02:34.530000Z",
  "file_hash": "4ead577fde5131271c5e408c397ab67df2ddaad358e3ba1f9e860886a7460556",
  "private": false,
  "record": {
    "abstract": "We investigate the set of completely positive, trace-nonincreasing linear\nmaps acting on the set M_N of mixed quantum states of size N. Extremal point of\nthis set of maps are characterized and its volume with respect to the\nHilbert-Schmidt (Euclidean) measure is computed explicitly for an arbitrary N.\nThe spectra of partially reduced rescaled dynamical matrices associated with\ntrace-nonincreasing completely positive maps belong to the N-cube inscribed in\nthe set of subnormalized states of size N. As a by-product we derive the\nmeasure in M_N induced by partial trace of mixed quantum states distributed\nuniformly with respect to HS-measure in $M_{N^2}$.",
    "arxiv_id": "quant-ph/0701143",
    "authors": [
      "Valerio Cappellini",
      "Hans-Juergen Sommers",
      "Karol Zyczkowski"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1063/1.2738359",
    "journal_ref": "J. Math. Phys. 48(5), 052110 (2007)",
    "title": "Subnormalized states and trace-nonincreasing maps",
    "url": "https://arxiv.org/abs/quant-ph/0701143"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2044b747-afcc-4ffb-9543-1864eac556e8",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}