{
  "annotation_id": "f9c7f1d0-7d59-42fd-9bfd-4a5c02c596e5",
  "date_created": "2026-03-02T18:02:13.635000Z",
  "date_modified": "2026-03-02T18:02:13.635000Z",
  "file_hash": "b2ee9cc131a03f9b70b7bc6ec1d590999bca6923fb0d4a3e496bc82d523ea89d",
  "private": false,
  "record": {
    "abstract": "We show that the analysis of entanglement distillation protocols for qudits\nof arbitrary dimension $D$ benefits from applying basic concepts from number\ntheory, since the set $\\zdn$ associated to Bell diagonal states is a module\nrather than a vector space. We find that a partition of $\\zdn$ into divisor\nclasses characterizes the invariant properties of mixed Bell diagonal states\nunder local permutations. We construct a very general class of recursion\nprotocols by means of unitary operations implementing these local permutations.\nWe study these distillation protocols depending on whether we use twirling\noperations in the intermediate steps or not, and we study them both\nanalitically and numerically with Monte Carlo methods. In the absence of\ntwirling operations, we construct extensions of the quantum privacy algorithms\nvalid for secure communications with qudits of any dimension $D$. When $D$ is a\nprime number, we show that distillation protocols are optimal both\nqualitatively and quantitatively.",
    "arxiv_id": "quant-ph/0503013",
    "authors": [
      "H. Bombin",
      "M. A. Martin-Delgado"
    ],
    "categories": [
      "quant-ph",
      "cond-mat.str-el",
      "hep-th",
      "physics.comp-ph"
    ],
    "doi": "10.1103/PhysRevA.72.032313",
    "title": "Entanglement Distillation Protocols and Number Theory",
    "url": "https://arxiv.org/abs/quant-ph/0503013"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "dab9bfb6-ebbc-4232-857a-265ba90ace2c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}