{
  "abstract": "Clifford circuits acting on product magic states provide a compact ansatz exhibiting extensive magic, volume-law entanglement, and even classically hard sampling under standard complexity assumptions. Here, we efficiently recover its hidden product subsystems from two-copy Bell sampling. Quadratic relations between Bell samples determine the irreducible blocks after removing Pauli stabilizers, and binary linear algebra constructs a Clifford disentangler. For logarithmic-size blocks, approximate learning of the full state is efficient whenever the state remains inverse-polynomially separated from acquiring additional Pauli stabilizers. We efficiently learn $n$-qubit states prepared by random $T$-doped Clifford circuits with $T$-gate density below one via $O(n^2)$ Bell samples, and disentangle hidden product blocks in Clifford-augmented matrix product states. For unitary learning, we exactly learn $T$-depth-one circuits using $O(n^2)$ queries. Finally, we rule out pseudorandom states and unitaries with a product bipartition hidden by Clifford circuits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27128",
  "author_total": 1,
  "authors": [
    {
      "name": "Tobias Haug"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/40y3kt2rthe6q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27128",
  "fulltext_url": null,
  "id": "40y3kt2rthe6q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27128",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7214172491",
  "pdf_url": "https://arxiv.org/pdf/2609.27128",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/40y3kt2rthe6q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.27128",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27128"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Efficient Learning of Clifford-Scrambled Product States",
  "title_text": "Efficient Learning of Clifford-Scrambled Product States",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:56Z",
  "url": "https://research.draconitic.com/paper/40y3kt2rthe6q",
  "venue": "arXiv",
  "versions": []
}