{
  "annotation_id": "e9f21052-895e-4728-a706-01ce2d4baea1",
  "date_created": "2026-03-02T18:01:42.643000Z",
  "date_modified": "2026-03-02T18:01:42.643000Z",
  "file_hash": "b5ae1c06705788387e71eab4cccb8195fb289549e7adcd748c68b9c8f67b52e7",
  "private": false,
  "record": {
    "abstract": "The majorization relation has been shown to be useful in classifying which\ntransformations of jointly held quantum states are possible using local\noperations and classical communication. In some cases, a direct transformation\nbetween two states is not possible, but it becomes possible in the presence of\nanother state (known as a catalyst); this situation is described mathematically\nby the trumping relation, an extension of majorization. The structure of the\ntrumping relation is not nearly as well understood as that of majorization. We\ngive an introduction to this subject and derive some new results. Most notably,\nwe show that the dimension of the required catalyst is in general unbounded;\nthere is no integer $k$ such that it suffices to consider catalysts of\ndimension $k$ or less in determining which states can be catalyzed into a given\nstate. We also show that almost all bipartite entangled states are potentially\nuseful as catalysts.",
    "arxiv_id": "quant-ph/0104058",
    "authors": [
      "Sumit Daftuar",
      "Matthew Klimesh"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.64.042314",
    "title": "The trumping relation and the structure of the bipartite entangled   states",
    "url": "https://arxiv.org/abs/quant-ph/0104058"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2d73a61c-0a3c-4eba-a8bb-7f2cb9ee219f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}