{
  "abstract": "Full tomography of a generic many-qubit quantum state requires exponentially many copies, while suitable structural constraints can make reconstruction sample-efficient. Existing approaches exploit, for example, limited entanglement structure, low magic, or constrained state-preparation circuits. Here we consider a class of mixed states that can simultaneously exhibit extensive entanglement and extensive magic. Specifically, we introduce Clifford-encoded block-product (CEBP) states, obtained by applying an unknown global Clifford unitary to a tensor product of arbitrary mixed states supported on unknown blocks of bounded size. We show that, for a fixed block size, CEBP states can be reconstructed using polynomially many copies by exploiting Clifford-preserved Pauli correlations to recover the latent structure and reduce the remaining problem to local tomography. Our result demonstrates that sample-efficient tomography can arise from bounded complexity in a latent frame even when the physical state is highly entangled, highly magical, and mixed, and suggests complexity modulo structured transformations as a broader organizing principle for quantum-state learnability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27177",
  "author_total": 2,
  "authors": [
    {
      "name": "Pengcheng Liao"
    },
    {
      "name": "Quntao Zhuang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2pgbqkz27mst9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27177",
  "fulltext_url": null,
  "id": "2pgbqkz27mst9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27177",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7214199938",
  "pdf_url": "https://arxiv.org/pdf/2609.27177",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2pgbqkz27mst9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.27177",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27177"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Sample-Efficient Tomography of a Class of Mixed States with Extensive Entanglement and Magic",
  "title_text": "Sample-Efficient Tomography of a Class of Mixed States with Extensive Entanglement and Magic",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:56Z",
  "url": "https://research.draconitic.com/paper/2pgbqkz27mst9",
  "venue": "arXiv",
  "versions": []
}