{
  "abstract": "Generative learning of a quantum measurement distribution from finite data requires choosing a model capacity that balances representation accuracy against estimation cost. We develop a bias-variance framework that decomposes the expected population Kullback-Leibler error at model capacity $s$ and sample size $N$ as $\\mathcal E(s,N)=B(s)+V(s,N)$, with representation bias $B$ and a variance term $V$ capturing the mean estimation error. In the well-sampled regime, $V(s,N)\\simeq[NC(s)]^{-1}$, and exponential or algebraic laws for $B$ and $C$ yield four scaling templates for the optimal error, from inverse powers of $N$ to inverse powers of $\\ln N$. For local autoregressive models, the context radius sets the model capacity, and $B$ is the summed conditional mutual information lost by truncating the context. For a smoothed histogram learner, we derive an exact finite-sample estimation cost that accounts for rarely observed contexts and recovers the parameter-count law in the well-sampled regime. For transverse-field Ising Born distributions, the independently evaluated bias and estimation cost predict both the optimal context radius and the optimal error. In the well-sampled regime, the estimation cost grows exponentially with context radius. Its competition with approximately exponential bias decay in the gapped regimes predicts power-law error decay in $N$, while algebraic bias decay at criticality predicts asymptotic inverse-power decay in $\\ln N$. Bulk-site results are consistent with the corresponding finite-sample predictions. These results connect the structure of quantum measurement distributions to the model capacity justified by finite data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38028",
  "author_total": 2,
  "authors": [
    {
      "name": "Shuhan Zhang"
    },
    {
      "name": "Yi-Zhuang You"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dt83aa4krvt3s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38028",
  "fulltext_url": null,
  "id": "dt83aa4krvt3s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38028",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38028",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dt83aa4krvt3s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.38028",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38028"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Sample Complexity for Generative Learning of Quantum Measurement Data",
  "title_text": "Sample Complexity for Generative Learning of Quantum Measurement Data",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:50Z",
  "url": "https://research.draconitic.com/paper/dt83aa4krvt3s",
  "venue": "arXiv",
  "versions": []
}