{
  "annotation_id": "0c62b2fc-a96a-416d-89a4-a59096eb6f08",
  "date_created": "2026-03-02T18:02:06.144000Z",
  "date_modified": "2026-03-02T18:02:06.144000Z",
  "file_hash": "a5c0160ff760dc6480964ab347d37372202aaaebb86ab16b2ffa580ccc2cea1d",
  "private": false,
  "record": {
    "abstract": "Off-diagonal long-range order (ODLRO) is a quantum phenomenon not describable\nin classical mechanical terms. It is believed to be one characteristic of\nsuperconductivity. The quantum state constructed by eta-pairing which\ndemonstrates ODLRO is an eigenstate of the three-dimensional Hubbard model.\nEntanglement is a key concept of the quantum information processing and has no\nclassical counterpart. We study the entanglement property of eta-pairing\nquantum state. The concurrence is a well-known measure of quantum entanglement.\nWe show that the concurrence of entanglement between one-site and the rest\nsites is exactly the correlation function of the ODLRO for the eta-pairing\nstate in the thermodynamic limit. So, when the eta-pairing state is entangled,\nit demonstrates ODLRO and is thus in superconducting phase, if it is a\nseparable state, there is no ODLRO. In the thermodynamic limit, the\nentanglement between M-site and other sites of the eta-pairing state does not\nvanish. Other types of ODLRO of eta-pairing state are presented. We show that\nthe behavior of the ODLRO correlation functions is equivalent to that of the\nentanglement of the eta-pairing state. The scaling of the entropy of the\nentanglement for the eta-pairing state is studied.",
    "arxiv_id": "quant-ph/0405130",
    "authors": [
      "Heng Fan",
      "Seth Lloyd"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.other"
    ],
    "doi": "10.1088/0305-4470/38/23/014",
    "journal_ref": "J.Phys.A38, (2005) 5285.",
    "title": "Entanglement of eta-pairing state with off-diagonal long-range order",
    "url": "https://arxiv.org/abs/quant-ph/0405130"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "efe61740-51d8-4fac-bb71-312d27c93d2a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}