{
  "annotation_id": "613609df-2d8d-4819-8ccd-395924a185be",
  "date_created": "2026-03-02T18:01:59.673000Z",
  "date_modified": "2026-03-02T18:01:59.673000Z",
  "file_hash": "33b6f378cbd04f9afdaeb48f0defc2671562d2bbe3bffca123225ee446a18b00",
  "private": false,
  "record": {
    "abstract": "The shape space of k labelled points on a plane can be identified with the\nspace of pure quantum states of dimension k-2. Hence, the machinery of quantum\nmechanics can be applied to the statistical analysis of planar configurations\nof points. Various correspondences between point configurations and quantum\nstates, such as linear superposition as well as unitary and stochastic\nevolution of shapes, are illustrated. In particular, a complete\ncharacterisation of shape eigenstates for an arbitrary number of points is\ngiven in terms of cyclotomic equations.",
    "arxiv_id": "quant-ph/0306013",
    "authors": [
      "Dorje C. Brody"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/37/1/017",
    "journal_ref": "Journal of Physics A37, 251-257 (2004)",
    "title": "Shapes of Quantum States",
    "url": "https://arxiv.org/abs/quant-ph/0306013"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "55a89041-bb2a-4471-b72a-021619f07e9b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}