{
  "annotation_id": "c7135f42-ec63-42e9-87cb-57b644346fed",
  "date_created": "2026-03-02T18:02:10.188000Z",
  "date_modified": "2026-03-02T18:02:10.188000Z",
  "file_hash": "7cb9312de84cd99e28e9f03ae871e76ea5034f24efb5974d431a850e829fe52a",
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  "record": {
    "abstract": "It is shown that generic N-party pure quantum states (with equidimensional\nsubsystems) are uniquely determined by their reduced states of just over half\nthe parties; in other words, all the information in almost all N-party pure\nstates is in the set of reduced states of just over half the parties. For N\neven, the reduced states in fewer than N/2 parties are shown to be an\ninsufficient description of almost all states (similar results hold when N is\nodd). It is noted that Real Algebraic Geometry is a natural framework for any\nanalysis of parts of quantum states: two simple polynomials, a quadratic and a\ncubic, contain all of their structure. Algorithmic techniques are described\nwhich can provide conditions for sets of reduced states to belong to pure or\nmixed states.",
    "arxiv_id": "quant-ph/0407117",
    "authors": [
      "Nick S. Jones",
      "Noah Linden"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.71.012324",
    "journal_ref": "Phys. Rev. A 71, 012324 (2005)",
    "title": "Parts of Quantum States",
    "url": "https://arxiv.org/abs/quant-ph/0407117"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "59e0c251-7b72-4bfb-a6f0-3a14c6a38325",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}