{
  "annotation_id": "9c757924-c11d-4508-8259-d4514f30ec1f",
  "date_created": "2026-03-02T18:01:42.319000Z",
  "date_modified": "2026-03-02T18:01:42.319000Z",
  "file_hash": "477b6f18bb88a0a2c60698d48c42ebbc0de7c45a025d6f9ca09e72113c8955f8",
  "private": false,
  "record": {
    "abstract": "We develop a theory of the algorithmic information in bits contained in an\nindividual pure quantum state. This extends classical Kolmogorov complexity to\nthe quantum domain retaining classical descriptions. Quantum Kolmogorov\ncomplexity coincides with the classical Kolmogorov complexity on the classical\ndomain. Quantum Kolmogorov complexity is upper bounded and can be effectively\napproximated from above under certain conditions. With high probability a\nquantum object is incompressible. Upper- and lower bounds of the quantum\ncomplexity of multiple copies of individual pure quantum states are derived and\nmay shed some light on the no-cloning properties of quantum states. In the\nquantum situation complexity is not sub-additive. We discuss some relations\nwith ``no-cloning\u0027\u0027 and ``approximate cloning\u0027\u0027 properties.",
    "arxiv_id": "quant-ph/0102108",
    "authors": [
      "Paul M. B. Vitanyi"
    ],
    "categories": [
      "quant-ph",
      "cs.CC",
      "cs.IT",
      "math.IT",
      "math.LO"
    ],
    "doi": "10.1109/18.945258",
    "journal_ref": "IEEE Transactions on Information Theory, Vol. 47, No. 6, September\n  2001, 2464-2479",
    "title": "Quantum Kolmogorov Complexity Based on Classical Descriptions",
    "url": "https://arxiv.org/abs/quant-ph/0102108"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5d2583f9-eb73-4495-82c3-2fd7c0d20d79",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}