{
  "annotation_id": "958be9b8-9189-4d48-b68b-7264bf68623b",
  "date_created": "2026-03-02T18:02:10.389000Z",
  "date_modified": "2026-03-02T18:02:10.389000Z",
  "file_hash": "e14713793340eaeef1d78aa0d29edcb2320503f783b649ffa494c188215d91a5",
  "private": false,
  "record": {
    "abstract": "We consider group-covariant positive operator valued measures (POVMs) on a\nfinite dimensional quantum system. Following Neumark\u0027s theorem a POVM can be\nimplemented by an orthogonal measurement on a larger system. Accordingly, our\ngoal is to find an implementation of a given group-covariant POVM by a quantum\ncircuit using its symmetry. Based on representation theory of the symmetry\ngroup we develop a general approach for the implementation of group-covariant\nPOVMs which consist of rank-one operators. The construction relies on a method\nto decompose matrices that intertwine two representations of a finite group. We\ngive several examples for which the resulting quantum circuits are efficient.\nIn particular, we obtain efficient quantum circuits for a class of POVMs\ngenerated by Weyl-Heisenberg groups. These circuits allow to implement an\napproximative simultaneous measurement of the position and crystal momentum of\na particle moving on a cyclic chain.",
    "arxiv_id": "quant-ph/0407054",
    "authors": [
      "Thomas Decker",
      "Dominik Janzing",
      "Martin Roetteler"
    ],
    "categories": [
      "quant-ph",
      "cs.ET"
    ],
    "doi": "10.1063/1.1827924",
    "journal_ref": "Journal of Mathematical Physics, 46:012104, 2005",
    "title": "Implementation of group-covariant POVMs by orthogonal measurements",
    "url": "https://arxiv.org/abs/quant-ph/0407054"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "272cf33a-08cc-4483-a687-3022568d60a9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}