{
  "annotation_id": "231fc6c8-c163-4783-a854-d18e7c3b0035",
  "date_created": "2026-03-02T18:01:49.454000Z",
  "date_modified": "2026-03-02T18:01:49.454000Z",
  "file_hash": "9c6737e49502da6c8270f9439c0d043555a3d8063d36239f58a8dbb36ada761e",
  "private": false,
  "record": {
    "abstract": "To implement any quantum operation (a.k.a. ``superoperator\u0027\u0027 or ``CP map\u0027\u0027)\non a d-dimensional quantum system, it is enough to apply a suitable overall\nunitary transformation to the system and a d^2-dimensional environment which is\ninitialized in a fixed pure state. It has been suggested that a d-dimensional\nenvironment might be enough if we could initialize the environment in a mixed\nstate of our choosing. In this note we show with elementary means that certain\nexplicit quantum operations cannot be realized in this way. Our counterexamples\nmap some pure states to pure states, giving strong and easily manageable\nconditions on the overall unitary transformation. Everything works in the more\ngeneral setting of quantum operations from d-dimensional to d\u0027-dimensional\nspaces, so we place our counterexamples within this more general framework.",
    "arxiv_id": "quant-ph/0111084",
    "authors": [
      "Christof Zalka",
      "Eleanor Rieffel"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1063/1.1499763",
    "journal_ref": "Journal of Mathematical Physics, Vol 43(9), September 2002, pp.\n  4376 - 4381",
    "title": "Quantum operations that cannot be implemented using a small mixed   environment",
    "url": "https://arxiv.org/abs/quant-ph/0111084"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f1f74a51-54ff-4672-83e0-5cfc8e573fac",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}