{
  "abstract": "Many tomography tasks require only a low-dimensional function of the state. We study local pure-state tomography under projective-fidelity access when a parametric model, a credible center, and a differentiable downstream task are known before acquisition. The pullback Fubini--Study metric and the task metric define coordinate-invariant generalized eigendirections, which we realize as a fixed library of geodesic fidelity probes. We prove two optimality results: the probe aligned with a task coordinate is its unique variance-minimizing location up to orientation, and, when prior and measurement information are diagonal in this basis, a diminishing-return greedy rule exactly minimizes the integer-budget local task-variance surrogate over the spectral library. Under common per-shot information and the stated large-budget condition, the absolute and relative gaps to arbitrary probe directions are respectively \\(O(B^{-3})\\) and \\(O(B^{-2})\\). A closed-form local estimator is followed by a task-metric localization projection that cannot increase quadratic task loss when localization holds. In six-qubit numerical experiments, the Schmidt-spectrum design activates only one or two settings and has lower mean task error than the post hoc best adaptive results across all tested dimensions and copy budgets. For full-state tomography, it likewise has lower mean infidelity throughout the tested local regime. The fixed batch uses no feedback loops and far fewer settings; under the illustrative latency model, its acquisition cost is roughly three to four orders of magnitude lower than that of the adaptive methods.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33723",
  "author_total": 2,
  "authors": [
    {
      "name": "Guy Hay"
    },
    {
      "name": "Nir Sharon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/74333b1yvn8jr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33723",
  "fulltext_url": null,
  "id": "74333b1yvn8jr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33723",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7224024788",
  "pdf_url": "https://arxiv.org/pdf/2610.33723",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/74333b1yvn8jr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.33723",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33723"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Task-Directed Spectral Design for Local Quantum Tomography",
  "title_text": "Task-Directed Spectral Design for Local Quantum Tomography",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:49Z",
  "url": "https://research.draconitic.com/paper/74333b1yvn8jr",
  "venue": "arXiv",
  "versions": []
}