{
  "abstract": "How many past requests are needed to decide which qubits should share entanglement? We show that the answer depends on the allocation choices created by the queries: a larger memory can require no more data. The memory stores a classical bit and answers requests through a fixed detector that preserves coherence within each measured sector. For independent commuting $X$- and $Z$-type Pauli queries, we characterize the full attainable prediction-contrast region and construct encodings that preserve the bit at every nonzero vertex. With sharp reports, a $d$-qubit path and groups of at most $k$ qubits have minimax excess error after $m$ requests proportional to $k^{-1}\\min\\{1,\\sqrt{d\\log(k+1)/m}\\}$, uniformly for $2\\leq k<d$. Connected biclique regions can grow without increasing sample demand when depth, region count and connections per region stay bounded. Preparation noise introduces a separate calibration requirement. We derive an exact tradeoff with extra fresh detector calls and transfer the learning law to structured transaction co-location. Population-risk experiments test the statistical predictions. We also compare encodings on a native 15-qubit device and learned partitions on public purchase baskets. The full chain wins on the device; frequency grouping outperforms basket search in the largest-capacity retail setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10141",
  "author_total": 1,
  "authors": [
    {
      "name": "Nathan Roll"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8tfs5f14b7ds3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10141",
  "fulltext_url": null,
  "id": "8tfs5f14b7ds3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10141",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7212194421",
  "pdf_url": "https://arxiv.org/pdf/2609.10141",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8tfs5f14b7ds3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.10141",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10141"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The Sample Complexity of Quantum Entanglement Allocation",
  "title_text": "The Sample Complexity of Quantum Entanglement Allocation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:12Z",
  "url": "https://research.draconitic.com/paper/8tfs5f14b7ds3",
  "venue": "arXiv",
  "versions": []
}