{
  "abstract": "Protocols for quantum state tomography can be characterized either by their sample complexity or by the tomographic rate function that governs the large deviation behaviour of error estimates. We establish a framework for the analysis of covariant protocols which allows us to compare these measures. First, we derive the rate functions for several protocols, including random purification-based protocols and the sample-optimal protocol of Haah et al. These rate functions are expressed in terms of a new family of divergences which includes the reverse sandwiched Rényi divergence and Keyl's annealed quantum relative entropy as special cases. We show that these rate functions obey a strict ordering, even though the sample complexity of each protocol is order optimal. We consider a different version of sample complexity based on Wasserstein distance rather than trace distance, and show that the ordering of the rate functions implies analogous strict inequalities for the Wasserstein-type sample complexity. Thus the tomographic rate function is a more fine-grained indicator of the performance of a tomography protocol than the usual sample complexity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40271",
  "author_total": 4,
  "authors": [
    {
      "name": "Arick Grootveld"
    },
    {
      "name": "Alexander Maloney"
    },
    {
      "name": "Jason Pollack"
    },
    {
      "name": "Peixue Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dykx7qxgcyhzg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40271",
  "fulltext_url": null,
  "id": "dykx7qxgcyhzg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40271",
  "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",
      "cs.IT"
    ],
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      "arxiv",
      "math-ph"
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      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.MP"
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      "arxiv",
      "math.PR"
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      "arxiv",
      "quant-ph"
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    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7215124900",
  "pdf_url": "https://arxiv.org/pdf/2609.40271",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dykx7qxgcyhzg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2609.40271",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40271"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Refined sample complexities from the tomographic rate function",
  "title_text": "Refined sample complexities from the tomographic rate function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/dykx7qxgcyhzg",
  "venue": "arXiv",
  "versions": []
}