{
  "annotation_id": "28520bc0-cd02-4b55-8be2-c1b8a1ac366b",
  "date_created": "2026-03-02T18:01:38.866000Z",
  "date_modified": "2026-03-02T18:01:38.866000Z",
  "file_hash": "788547f45364d4d50d65d5d92978a8c247f879e1528028e9029d4c416726c943",
  "private": false,
  "record": {
    "abstract": "This paper develops a geometric model for coupled two-state quantum systems\n(qubits), which is formulated using geometric (aka Clifford) algebra. It begins\nby showing how Euclidean spinors can be interpreted as entities in the\ngeometric algebra of a Euclidean vector space. This algebra is then lifted to\nMinkowski space-time and its associated geometric algebra, and the insights\nthis provides into how density operators and entanglement behave under Lorentz\ntransformations are discussed. The direct sum of multiple copies of space-time\ninduces a tensor product structure on the associated algebra, in which a\nsuitable quotient is isomorphic to the matrix algebra conventionally used in\nmulti-qubit quantum mechanics. Finally, the utility of geometric algebra in\nunderstanding both unitary and nonunitary quantum operations is demonstrated on\nseveral examples of interest in quantum information processing.",
    "arxiv_id": "quant-ph/0004031",
    "authors": [
      "Timothy F. Havel",
      "Chris J. L. Doran"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Geometric Algebra in Quantum Information Processing",
    "url": "https://arxiv.org/abs/quant-ph/0004031"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "08040d2b-5021-420e-8db9-c6cb02fc40be",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}