{
  "abstract": "We bound local quantum leakage from Shamir sharing uniformly over prime fields and permitted share-dependent channels. The adversary receives all outputs and a reference to a resource independent of the secret and sharing randomness. For independent device-reference pairs at fixed output dimension, we determine the exact exponent of the worst-case trace distance for two chosen secrets at every fixed reconstruction rate above one half, including its dependence on entanglement within each pair. For unentangled one-qubit leakage, this improves the sufficient rate of about $0.7334$ proved by Batra et al. Above one half, we also determine the exact exponent when an arbitrarily entangled support is tensored with single-device states elsewhere. Every fixed support fraction below the reconstruction rate gives exponential security, while a reconstruction set admits a known attack. Exponential security extends to fixed finite-memory processes with primitive transfer channels, fixed stationary chains satisfying upper operator mixing, and canonical primitive matrix product states, allowing arbitrary finite adversary extensions of the device marginal. For one-qubit outputs, fully separable resources and independent pairs whose joint output-reference states are positive under partial transpose for every share admit rates slightly below one half.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06350",
  "author_total": 2,
  "authors": [
    {
      "name": "Isaac Barouch Essayag"
    },
    {
      "name": "Aryeh Lev Zabokritskiy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2s4t4b1fvzyja.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06350",
  "fulltext_url": null,
  "id": "2s4t4b1fvzyja",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06350",
  "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 Information and Cryptography"
    ]
  ],
  "openalex": "W7220689472",
  "pdf_url": "https://arxiv.org/pdf/2610.06350",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2s4t4b1fvzyja.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.06350",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06350"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Leakage from Shamir Sharing with Correlated Resources",
  "title_text": "Quantum Leakage from Shamir Sharing with Correlated Resources",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:15Z",
  "url": "https://research.draconitic.com/paper/2s4t4b1fvzyja",
  "venue": "arXiv",
  "versions": []
}