{
  "annotation_id": "a9d1f662-879a-402a-8749-c259997c9d1e",
  "date_created": "2026-03-02T18:01:42.187000Z",
  "date_modified": "2026-03-02T18:01:42.187000Z",
  "file_hash": "3696340b5283ff5bce1f449cc57906fd0f5dd797a4c096b6b189025030716b2b",
  "private": false,
  "record": {
    "abstract": "We consider several problems that involve finding the eigenvalues and\ngenerating the eigenstates of unknown unitary gates. We first examine\nControlled-U gates that act on qubits, and assume that we know the eigenvalues.\nIt is then shown how to use singlet states to produce qubits in the eigenstates\nof the gate. We then remove the assumption that we know the eigenvalues and\nshow how to both find the eigenvalues and produce qubits in the eigenstates.\nFinally, we look at the case where the unitary operator acts on qutrits and has\neigenvalues of 1 and -1, where the eigenvalue 1 is doubly degenerate. The\neigenstates are unknown. We are able to use a singlet state to produce a qutrit\nin the eigenstate corresponding to the -1 eigenvalue.",
    "arxiv_id": "quant-ph/0104107",
    "authors": [
      "Mark Hillery",
      "Vladimir Buzek"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.64.042303",
    "title": "Singlet states and the estimation of eigenstates and eigenvalues of an   unknown Controlled-U gate",
    "url": "https://arxiv.org/abs/quant-ph/0104107"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2225b771-8a72-4733-bd52-068ed545aedd",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}