{
  "abstract": "Quantum channel tomography (also known as quantum process tomography) is a fundamental task in quantum information and quantum computing, aiming to learn the full description of an unknown quantum channel from black-box queries. For channels with input dimension $d_1$, output dimension $d_2$, and Kraus rank at most $r$, [CGO+26] identifies the dilation rate $τ=rd_2/d_1\\geq 1$ as a key parameter governing a Heisenberg-to-classical transition in query complexity. While the optimal bounds in the boundary regime ($τ=1$) and the away-from-boundary regime ($τ\\geq 1+Ω(1)$) are now known, the precise behavior in the near-boundary regime ($1<τ<1+o(1)$) has remained unresolved. In this paper, we close this gap, thereby fully settling the query complexity of quantum channel tomography. Specifically, we show that the query complexity is - $Ω(rd_1d_2/\\varepsilon^2)$ for diamond norm error $\\varepsilon$, matching the upper bound by [MB26, CGO+26], - $Θ(d_1^2/\\varepsilon+\\min\\{(τ-1)d_1^2,(τ-1)^2d_1^2d_2^2\\}/\\varepsilon^2)$ for Choi trace norm error $\\varepsilon$. Our results reveal two qualitatively different forms of the Heisenberg-to-classical transition. For diamond norm tomography, the Heisenberg scaling disappears suddenly as soon as $τ$ leaves the boundary regime. In contrast, Choi trace norm tomography exhibits a gradual transition from Heisenberg to classical scaling as $τ$ moves from the boundary regime to the away-from-boundary regime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03639",
  "author_total": 2,
  "authors": [
    {
      "name": "Kean Chen"
    },
    {
      "name": "Aadil Oufkir"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/15qbq3txpawf3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03639",
  "fulltext_url": null,
  "id": "15qbq3txpawf3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03639",
  "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",
      "math.IT"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03639",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/15qbq3txpawf3.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:04Z",
      "native_id": "2611.03639",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03639"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum channel tomography: optimal bounds in the near-boundary regime",
  "title_text": "Quantum channel tomography: optimal bounds in the near-boundary regime",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/15qbq3txpawf3",
  "venue": "arXiv",
  "versions": []
}