{
  "annotation_id": "59f7f87f-0bfe-4b7c-a7de-adb7b8840e8b",
  "date_created": "2026-03-02T18:01:42.600000Z",
  "date_modified": "2026-03-02T18:01:42.600000Z",
  "file_hash": "5eaed2a9feaca5db8fac02bc94b5cbe4dbe3a0ca2dbe48ea4622787ee030613d",
  "private": false,
  "record": {
    "abstract": "We extend algorithmic information theory to quantum mechanics, taking a\nuniversal semicomputable density matrix (``universal probability\u0027\u0027) as a\nstarting point, and define complexity (an operator) as its negative logarithm.\n  A number of properties of Kolmogorov complexity extend naturally to the new\ndomain. Approximately, a quantum state is simple if it is within a small\ndistance from a low-dimensional subspace of low Kolmogorov complexity. The von\nNeumann entropy of a computable density matrix is within an additive constant\nfrom the average complexity. Some of the theory of randomness translates to the\nnew domain.\n  We explore the relations of the new quantity to the quantum Kolmogorov\ncomplexity defined by Vitanyi (we show that the latter is sometimes as large as\n2n - 2log n and the qubit complexity defined by Berthiaume, Dam and Laplante.\nThe ``cloning\u0027\u0027 properties of our complexity measure are similar to those of\nqubit complexity.",
    "arxiv_id": "quant-ph/0011046",
    "authors": [
      "Peter Gacs"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/34/35/312",
    "journal_ref": "J. Phys. A: Math. Gen., 34:1--22, 2001",
    "title": "Quantum Algorithmic Entropy",
    "url": "https://arxiv.org/abs/quant-ph/0011046"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "61018f44-ef56-480a-8a07-89bdadf67452",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}