{
  "annotation_id": "d287a806-6d95-4b57-b8ca-4221032bffd6",
  "date_created": "2026-03-02T18:02:26.594000Z",
  "date_modified": "2026-03-02T18:02:26.594000Z",
  "file_hash": "fade884bd1ea0cd3be69b0a9a7045139a145d09ea7feb374f5a29f07ffbbc159",
  "private": false,
  "record": {
    "abstract": "We study geometrical aspects of entanglement, with the Hilbert--Schmidt norm\ndefining the metric on the set of density matrices. We focus first on the\nsimplest case of two two-level systems and show that a ``relativistic\u0027\u0027\nformulation leads to a complete analysis of the question of separability. Our\napproach is based on Schmidt decomposition of density matrices for a composite\nsystem and non-unitary transformations to a standard form. The positivity of\nthe density matrices is crucial for the method to work. A similar approach\nworks to some extent in higher dimensions, but is a less powerful tool. We\nfurther present a numerical method for examining separability, and illustrate\nthe method by a numerical study of bound entanglement in a composite system of\ntwo three-level systems.",
    "arxiv_id": "quant-ph/0605079",
    "authors": [
      "Jon Magne Leinaas",
      "Jan Myrheim",
      "Eirik Ovrum"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.74.012313",
    "title": "Geometrical aspects of entanglement",
    "url": "https://arxiv.org/abs/quant-ph/0605079"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8a56a173-5c43-44d6-a2ae-060c3ae21a55",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}