{
  "abstract": "We study state tomography when each measurement acts on at most $k$ fresh copies and no quantum memory is retained between blocks. We prove a lower bound matching the upper bound in [arXiv:2510.07788]. Thus the copy complexity of estimating an arbitrary $d$-dimensional state to trace distance $ε$ is, up to absolute constant factors, $\\max\\{d^3/(\\sqrt{k}ε^2),d^2/ε^2\\}$ for every $k$ and all sufficiently small $ε$. This removes the earlier restriction that $k$ be small as a function of the accuracy. The lower bound applies to arbitrary measurements within each block and adaptive choices between blocks. The lower bound already applies in a small neighborhood of any state whose smallest eigenvalue is of order $1/d$, even when the center is known. The main ingredient is a uniform Fisher information bound for one measurement block that depends only on the smallest eigenvalue of the state. The proof avoids the perturbative expansion responsible for the restriction in [arXiv:2402.16353]. Fano's inequality for metric balls and a log-Sobolev comparison between mutual and Fisher information then reduce the adaptive protocol to this block bound [arXiv:1607.00550, arXiv:1902.08582].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05718",
  "author_total": 4,
  "authors": [
    {
      "name": "Ufuk Keskin"
    },
    {
      "name": "Jason Luo"
    },
    {
      "name": "Mahbod Majid"
    },
    {
      "name": "Matthew Radzihovsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8x62zgkqcg9d0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05718",
  "fulltext_url": null,
  "id": "8x62zgkqcg9d0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05718",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7212072900",
  "pdf_url": "https://arxiv.org/pdf/2609.05718",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8x62zgkqcg9d0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.05718",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05718"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Tight Lower Bounds for State Tomography with Limited Entanglement",
  "title_text": "Tight Lower Bounds for State Tomography with Limited Entanglement",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/8x62zgkqcg9d0",
  "venue": "arXiv",
  "versions": []
}