{
  "annotation_id": "3cd4799b-762d-4b5d-a889-be4408dcb8c6",
  "date_created": "2026-03-02T18:01:42.320000Z",
  "date_modified": "2026-03-02T18:01:42.320000Z",
  "file_hash": "46c3ec70ddd2bfbc6084c4bd81656fa830050062a28dbc68d3cb889c85f5ab62",
  "private": false,
  "record": {
    "abstract": "We generalise our previous results of universal linear manipulations [Phys.\nRev. A63, 032304 (2001)] to investigate three types of nonlinear qubit\ntransformations using measurement and quantum based schemes. Firstly, nonlinear\nrotations are studied. We rotate different parts of a Bloch sphere in opposite\ndirections about the z-axis. The second transformation is a map which sends a\nqubit to its orthogonal state (which we define as ORTHOG). We consider the case\nwhen the ORTHOG is applied to only a partial area of a Bloch sphere. We also\nstudy nonlinear general transformation, i.e. (theta,phi)-\u003e(theta-alpha,phi),\nagain, applied only to part of the Bloch sphere. In order to achieve these\nthree operations, we consider different measurement preparations and derive the\noptimal average (instead of universal) quantum unitary transformations. We also\nintroduce a simple method for a qubit measurement and its application to other\ncases.",
    "arxiv_id": "quant-ph/0102100",
    "authors": [
      "Lucien Hardy",
      "David D. Song"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.64.032301",
    "journal_ref": "Phys. Rev. A 64, 032301 (2001)",
    "title": "Nonlinear Qubit Transformations",
    "url": "https://arxiv.org/abs/quant-ph/0102100"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "507dc017-1965-4d3b-a67d-8e7f4ad15766",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}