{
  "annotation_id": "d8fede23-4fe0-48e0-a061-191580986353",
  "date_created": "2026-03-02T18:01:42.576000Z",
  "date_modified": "2026-03-02T18:01:42.576000Z",
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  "private": false,
  "record": {
    "abstract": "The Pauli operators (tensor products of Pauli matrices) provide a complete\nbasis of operators on the Hilbert space of N qubits. We prove that the set of\n4^N-1 Pauli operators may be partitioned into 2^N+1 distinct subsets, each\nconsisting of 2^N-1 internally commuting observables. Furthermore, each such\npartitioning defines a unique choice of 2^N+1 mutually unbiased basis sets in\nthe N-qubit Hilbert space. Examples for 2 and 3 qubit systems are discussed\nwith emphasis on the nature and amount of entanglement that occurs within these\nbasis sets.",
    "arxiv_id": "quant-ph/0104012",
    "authors": [
      "Jay Lawrence",
      "Caslav Brukner",
      "Anton Zeilinger"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.65.032320",
    "journal_ref": "Phys. Rev. A 65, 032320 (2002)",
    "title": "Mutually unbiased binary observable sets on N qubits",
    "url": "https://arxiv.org/abs/quant-ph/0104012"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1ca6156c-68aa-44e9-9cee-670728b241e7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}