{
  "annotation_id": "9e98367e-a163-44ff-8f64-4a796ad260a2",
  "date_created": "2026-03-02T18:02:43.878000Z",
  "date_modified": "2026-03-02T18:02:43.878000Z",
  "file_hash": "bb6b70831ef89f9f5282b02870dc33120b41481116b516786d8ca9dd457a80bb",
  "private": false,
  "record": {
    "abstract": "Under the name prime decomposition (pd), a unique decomposition of an\narbitrary $N$-dimensional density matrix $\\rho$ into a sum of seperable density\nmatrices with dimensions given by the coprime factors of $N$ is introduced. For\na class of density matrices a complete tensor product factorization is\nachieved. The construction is based on the Chinese Remainder Theorem and the\nprojective unitary representation of $Z_N$ by the discrete Heisenberg group\n$H_N$. The pd isomorphism is unitarily implemented and it is shown to be\ncoassociative and to act on $H_N$ as comultiplication. Density matrices with\ncomplete pd are interpreted as grouplike elements of $H_N$. To quantify the\ndistance of $\\rho$ from its pd a trace-norm correlation index $\\cal E$ is\nintroduced and its invariance groups are determined.",
    "arxiv_id": "quant-ph/9806007",
    "authors": [
      "D. Ellinas",
      "E. G. Floratos"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP",
      "math.QA"
    ],
    "doi": "10.1088/0305-4470/32/5/001",
    "journal_ref": "J.Phys.A32:L63-L69,1999",
    "title": "Prime decomposition and correlation measure of finite quantum systems",
    "url": "https://arxiv.org/abs/quant-ph/9806007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a934bd9e-55d2-4ec1-ad34-1ffadfbe79d5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}