{
  "annotation_id": "a58b79b1-c6c0-4138-a71c-129d15419793",
  "date_created": "2026-03-02T18:01:45.122000Z",
  "date_modified": "2026-03-02T18:01:45.122000Z",
  "file_hash": "ffd927f132588805e1d1cbae60d63a34311f524f2904a447c1022a39277a9ee3",
  "private": false,
  "record": {
    "abstract": "We discuss a generalization to 2 qubits of the standard Bloch sphere\nrepresentation for a single qubit, in the framework of Hopf fibrations of high\ndimensional spheres by lower dimensional spheres. The single qubit Hilbert\nspace is the 3-dimensional sphere S3. The S2 base space of a suitably oriented\nS3 Hopf fibration is nothing but the Bloch sphere, while the circular fibres\nrepresent the qubit overall phase degree of freedom. For the two qubits case,\nthe Hilbert space is a 7-dimensional sphere S7, which also allows for a Hopf\nfibration, with S3 fibres and a S4 base. A main striking result is that\nsuitably oriented S7 Hopf fibrations are entanglement sensitive. The relation\nwith the standard Schmidt decomposition is also discussed",
    "arxiv_id": "quant-ph/0108137",
    "authors": [
      "R. Mosseri",
      "R. Dandoloff"
    ],
    "categories": [
      "quant-ph",
      "cond-mat"
    ],
    "doi": "10.1088/0305-4470/34/47/324",
    "title": "Geometry of entangled states, Bloch spheres and Hopf fibrations",
    "url": "https://arxiv.org/abs/quant-ph/0108137"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "92c9aaf6-d372-4389-847a-adf0281aade5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}