{
  "annotation_id": "bdc60499-0c13-46e2-99a3-7a02411c3ab7",
  "date_created": "2026-03-02T18:02:24.248000Z",
  "date_modified": "2026-03-02T18:02:24.248000Z",
  "file_hash": "65291de0ba6f840ae55f879a9b813deaa8948f16775839b0368880d0a0467c6e",
  "private": false,
  "record": {
    "abstract": "Using the SU($N$) representation of the group theory, we derive the general\nform of the spin swapping operator for the quantum Heisenberg spin-$s$ systems.\nWe further prove that such a spin swapping operator is equal to the spin\nsinglet pairing operator under the partial transposition. For SU(2) invariant\nstates, it is shown that the expectation value of the spin swapping operator\nand its generalizations, the permutations, can be used as an entanglement\nwitness, especially, for the formulation of observable conditions of\nentanglement.",
    "arxiv_id": "quant-ph/0601129",
    "authors": [
      "Guang-Ming Zhang",
      "Xiaoguang Wang"
    ],
    "categories": [
      "quant-ph",
      "astro-ph",
      "cond-mat.stat-mech"
    ],
    "doi": "10.1088/0305-4470/39/26/017",
    "journal_ref": "J.Phys. A39 (2006) 8515",
    "title": "Swapping and permutation operators as entanglement witnesses for quantum   Heisenberg spin-$s$ systems",
    "url": "https://arxiv.org/abs/quant-ph/0601129"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7a676d49-ddfc-48ba-95f1-57d687e3b3cb",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}