{
  "annotation_id": "89e71c05-6471-40e4-b4a4-fbd7416bae8e",
  "date_created": "2026-03-02T18:02:33.708000Z",
  "date_modified": "2026-03-02T18:02:33.708000Z",
  "file_hash": "121bfffbaf14d306c30be0d9d8edcbae304a3904acb901e51f53e2c69a444ee1",
  "private": false,
  "record": {
    "abstract": "We present an extremal result for the class of graphs G which (together with\nsome specified sets of input and output vertices, I and O) have a certain\n\"flow\" property introduced by Danos and Kashefi for the one-way measurement\nmodel of quantum computation. The existence of a flow for a triple (G,I,O)\nallows a unitary embedding to be derived from any choice of measurement bases\nallowed in the one-way measurement model. We prove an upper bound on the number\nof edges that a graph G may have, in order for a triple (G,I,O) to have a flow\nfor some $I, O \\subseteq V(G)$, in terms of the number of vertices in G and O.\nThis implies that finding a flow for a triple (G,I,O) when |I| = |O| = k\n(corresponding to unitary transformations in the measurement model) and |V(G)|\n= n can be performed in time O(k^2 n), improving the earlier known bound of\nO(km) given in [quant-ph/0611284], where m = |E(G)|.",
    "arxiv_id": "quant-ph/0702229",
    "authors": [
      "Niel de Beaudrap",
      "Martin Pei"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "An extremal result for geometries in the one-way measurement model",
    "url": "https://arxiv.org/abs/quant-ph/0702229"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cc484347-075e-4bf6-a3d9-2a71504c4453",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}