{
  "abstract": "One should not assume that reconstructing an electronic observable with a smaller set of measurement settings will cut the number of repetitions in proportion. Each setting is simply a basis change and qubit readout, but the savings are not guaranteed to be commensurate. Take two electrons of opposite spin in two spatial orbitals: the orbital degree of freedom of each electron acts as a logical qubit and rotations are independent in the spin sectors. From the observable's one- and two-qubit coefficients we derive an exact floor for the setting count and a decomposition to meet it in no more than three settings. With fewer settings, the minimum error in the two-qubit correlation coefficients is set by the singular values left out. A case in point is an exchange with equal nonzero couplings on the three Pauli axes. This demands three orbital settings yet only one joint measurement. We offer a Clifford circuit for four physical qubits to effect the necessary mapping of Pauli products under conjugation. In the case of a one-parameter family of logical singlet-triplet mixtures, the orbital-to-Clifford shot cost ratio is three at maximum mixing and trends toward 3/2 near the logical singlet. Where spin sectors may be mixed, isotropic exchange needs one orbital setting. For spin-conserving Hamiltonians with $N$ spatial orbitals encoded via Jordan-Wigner, the $X$-rank, the binary rank of the $X$ parts of its strings, of any commuting Pauli string family is no more than $2(N-1)$. Searches with the Robust Adaptive Nature-inspired Global Explorer (RANGE) reach this limit for CH$_4$, with the rank of the Hamiltonian support vouching for the maximality of the search values. And for all nonidentity Pauli strings on $n$ qubits, semidefinite witnesses from the Lovász theta number give a lower bound on the Clifford setting count that agrees with the integer cover and counting bounds at $2^n+1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.16869",
  "author_total": 2,
  "authors": [
    {
      "name": "Federico Zahariev"
    },
    {
      "name": "Vanda Glezakou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1s2dx7hksjm2d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.16869",
  "fulltext_url": null,
  "id": "1s2dx7hksjm2d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.16869",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "physics.chem-ph"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7169846105",
  "pdf_url": "https://arxiv.org/pdf/2607.16869",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1s2dx7hksjm2d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2607.16869",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.16869"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Beyond Orbital Rotations: Correlation-Rank Limits and Clifford-Accessible Measurement, from Algebra and Global Optimization",
  "title_text": "Beyond Orbital Rotations: Correlation-Rank Limits and Clifford-Accessible Measurement, from Algebra and Global Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:36Z",
  "url": "https://research.draconitic.com/paper/1s2dx7hksjm2d",
  "venue": "arXiv",
  "versions": []
}