{
  "annotation_id": "be408b90-6fb4-43cb-b4ce-a7c0789cd75e",
  "date_created": "2026-03-02T18:02:30.425000Z",
  "date_modified": "2026-03-02T18:02:30.425000Z",
  "file_hash": "f38c2aa74cbc9c541724cd4e191419af68d03c2daf04429e406e87fdc9400c26",
  "private": false,
  "record": {
    "abstract": "Schur duality decomposes many copies of a quantum state into subspaces\nlabeled by partitions, a decomposition with applications throughout quantum\ninformation theory. Here we consider applying Schur duality to the problem of\ndistinguishing coset states in the standard approach to the hidden subgroup\nproblem. We observe that simply measuring the partition (a procedure we call\nweak Schur sampling) provides very little information about the hidden\nsubgroup. Furthermore, we show that under quite general assumptions, even a\ncombination of weak Fourier sampling and weak Schur sampling fails to identify\nthe hidden subgroup. We also prove tight bounds on how many coset states are\nrequired to solve the hidden subgroup problem by weak Schur sampling, and we\nrelate this question to a quantum version of the collision problem.",
    "arxiv_id": "quant-ph/0609110",
    "authors": [
      "Andrew M. Childs",
      "Aram W. Harrow",
      "Pawel Wocjan"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/978-3-540-70918-3_51",
    "journal_ref": "Proc. 24th Symposium on Theoretical Aspects of Computer Science\n  (STACS 2007), Lecture Notes in Computer Science 4393, pp. 598-609",
    "title": "Weak Fourier-Schur sampling, the hidden subgroup problem, and the   quantum collision problem",
    "url": "https://arxiv.org/abs/quant-ph/0609110"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "d140a9da-242b-419f-a2be-95b23f4ebe99",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}