{
  "annotation_id": "65207589-615f-4dd1-af1a-d9af7a62b96e",
  "date_created": "2026-03-02T18:02:17.041000Z",
  "date_modified": "2026-03-02T18:02:17.041000Z",
  "file_hash": "15c44939ea81837cd1564c4e1b4d564ff505541a4405a150957fcaed62e12b80",
  "private": false,
  "record": {
    "abstract": "We consider the problem of estimating an SU(d) quantum operation when n\ncopies of it are available at the same time. It is well known that, if one uses\na separable state as the input for the unitaries, the optimal mean square error\nwill decrease as 1/n. However it is shown here that, if a proper entangled\nstate is used, the optimal mean square error will decrease at a 1/n^2 rate. It\nis also shown that spherical 2-designs (e.g. complete sets of mutually unbiased\nbases and symmetric informationally complete positive operator valued measures)\ncan be used to design optimal input states. Although 2-designs are believed to\nexist for every dimension, this has not yet been proven. Therefore, we give an\nalternative input state based on approximate 2-designs which can be made\narbitrarily close to optimal. It is shown that measurement strategies which are\nbased on local operations and classical communication between the ancilla and\nthe rest of the system can be optimal.",
    "arxiv_id": "quant-ph/0507073",
    "authors": [
      "Manuel A. Ballester"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Optimal estimation of SU(d) using exact and approximate 2-designs",
    "url": "https://arxiv.org/abs/quant-ph/0507073"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2ea4234a-2f1c-474e-93a4-b5034df7a695",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}