{
  "annotation_id": "79e78f85-9089-4e9e-9beb-da6f522ca5b4",
  "date_created": "2026-03-02T18:02:10.466000Z",
  "date_modified": "2026-03-02T18:02:10.466000Z",
  "file_hash": "c61e9ac2aa82bc769b808e263e939312a9a6e3bf6035aed1cdfdc007879aa2c5",
  "private": false,
  "record": {
    "abstract": "We discuss existence of mixed state of multicomponent system with given\nspectrum and given reduced density matrices. We give a complete solution of the\nproblem in terms of linear inequalities on the spectra, accompanied with\nextensive tables of marginal inequalities, including arrays up to 4 qubits. In\nthe second part of the paper we pursue another approach based on reduction of\nthe problem to representation theory of the symmetric group.",
    "arxiv_id": "quant-ph/0409113",
    "authors": [
      "Alexander Klyachko"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Quantum marginal problem and representations of the symmetric group",
    "url": "https://arxiv.org/abs/quant-ph/0409113"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4ab0cd4b-ee7a-437f-8b18-7bb118b067de",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}