{
  "annotation_id": "ab576f39-d35b-47d8-84e1-d2a8411f7564",
  "date_created": "2026-03-02T18:02:48.590000Z",
  "date_modified": "2026-03-02T18:02:48.590000Z",
  "file_hash": "64af5d5bd0a3fc6cafbf928338aae626a603a6301c51ae9722898296750138fc",
  "private": false,
  "record": {
    "abstract": "We consider a Quantum Computer with n quantum-bits (`qubits\u0027), where each\nqubit is coupled independently to an environment affecting the state in a\ndephasing or depolarizing way. For mixed states we suggest a quantification for\nthe property of showing {\\it quantum} uncertainty on the macroscopic level. We\nillustrate in which sense a large parameter can be seen as an indicator for\nlarge entanglement and give hypersurfaces enclosing the set of separable\nstates. Using methods of the classical theory of maximum likelihood estimation\nwe prove that this parameter is decreasing with 1/\\sqrt{n} for all those states\nwhich have been exposed to the environment.\n  Furthermore we consider a Quantum Computer with perfect 1-qubit gates and\n2-qubit gates with depolarizing error and show that any state which can be\nobtained from a separable initial state lies inbetween a family of pairs of\ncertain hypersurfaces parallel to those enclosing the separable ones.",
    "arxiv_id": "quant-ph/9907042",
    "authors": [
      "Dominik Janzing",
      "Thomas Beth"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.61.052308",
    "journal_ref": "Phys.Rev.A61:052308,2000",
    "title": "Fragility of a class of highly entangled states of many quantum-bits",
    "url": "https://arxiv.org/abs/quant-ph/9907042"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e90a8d0e-c891-4a96-8f13-cc3dc88ab05c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}