{
  "annotation_id": "44ed4df9-2509-4d37-943e-147a5b6a282f",
  "date_created": "2026-03-02T18:02:41.657000Z",
  "date_modified": "2026-03-02T18:02:41.657000Z",
  "file_hash": "b082dff1d1e7230e8ce2c75e194d3c6a322a41f5109d04893758656a6c1f7baa",
  "private": false,
  "record": {
    "abstract": "The quantum state space $\\cal S$ over a $d$-dimensional Hilbert space is\nrepresented as a convex subset of a $D-1$-dimensional sphere $S_{D-1}\\subset\n{\\bf{R}}^D$, where $D=d^2-1.$ Quantum tranformations (CP-maps) are then\nassociated with the affine transformations of ${\\bf{R}}^D,$ and $N\\mapsto M$\n{\\it cloners} induce polynomial mappings. In this geometrical setting it is\nshown that an optimal cloner can be chosen covariant and induces a map between\nreduced density matrices given by a simple contraction of the associated\n$D$-dimensional Bloch vectors.",
    "arxiv_id": "quant-ph/9804011",
    "authors": [
      "Paolo Zanardi"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.58.3484",
    "journal_ref": "Phys.Rev. A58 (1998) 3484",
    "title": "Quantum Cloning in $d$ dimensions",
    "url": "https://arxiv.org/abs/quant-ph/9804011"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2adbb5e2-0755-4dc4-9161-0c035b99058f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}