{
  "annotation_id": "a4050836-03b6-4016-bad0-66753e2dbbc5",
  "date_created": "2026-03-02T18:02:31.150000Z",
  "date_modified": "2026-03-02T18:02:31.150000Z",
  "file_hash": "c8667fa26766f8f5e29f7ea70850bc4b53dc008df39b58111fdd8e101842a77f",
  "private": false,
  "record": {
    "abstract": "We make a geometric study of the phases acquired by a general pure bipartite\ntwo level system after a cyclic unitary evolution. The geometric representation\nof the two particle Hilbert space makes use of Hopf fibrations. It allows for a\nsimple description of the dynamics of the entangled state\u0027s phase during the\nwhole evolution. The global phase after a cyclic evolution is always an entire\nmultiple of $\\pi$ for all bipartite states, a result that does not depend on\nthe degree of entanglement. There are three different types of phases combining\nthemselves so as to result in the $n \\pi$ global phase. They can be identified\nas dynamical, geometrical and topological. Each one of them can be easily\nidentified using the presented geometric description. The interplay between\nthem depends on the initial state and on its trajectory and the results\nobtained are shown to be in connection to those on mixed states phases.",
    "arxiv_id": "quant-ph/0608114",
    "authors": [
      "P\u00e9rola Milman"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.73.062118",
    "journal_ref": "Phys. Rev. A 73, 062118 (2006)",
    "title": "Phase Dynamics of Two Entangled Qubits",
    "url": "https://arxiv.org/abs/quant-ph/0608114"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "356c96c8-668f-41a7-855f-072886dafdf1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}