{
  "abstract": "Quantum resource distillation converts imperfect resource states into highly resourceful targets and is a central task in quantum information processing. When distillation is probabilistic, unfavorable outcomes may be discarded and the quality of the output is evaluated conditioned on success, leading to a notion of reliability that differs from the deterministic setting. Here we study the conditional error exponents of probabilistic quantum resource distillation under approximately resource-nongenerating instruments and derive its general connection to the postselected composite quantum hypothesis testing against the corresponding set of free states. This reduction leads naturally to scale-invariant projective distinguishability measures and provides finite-blocklength bounds for a broad class of resource theories. We apply the framework to entanglement, coherence, and magic. For entanglement and magic, we obtain exact zero-rate asymptotic characterizations of the conditional error exponent in terms of regularized projective distinguishability, while for coherence we derive general finite-blocklength and asymptotic bounds. For representative entangled and magic states, the resulting quantities can be evaluated analytically and reveal regimes in which postselection yields a strictly larger conditional error exponent than deterministic distillation. Furthermore, we also show that the conditional error exponents for probabilistic entanglement distillation under a strictly positive success probability constraint are smaller than those with no constraints on the success probability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06688",
  "author_total": 1,
  "authors": [
    {
      "name": "Xian Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4ms28e7mcge8g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06688",
  "fulltext_url": null,
  "id": "4ms28e7mcge8g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06688",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7212001525",
  "pdf_url": "https://arxiv.org/pdf/2609.06688",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4ms28e7mcge8g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2609.06688",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06688"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Conditional Error Exponents of Probabilistic Quantum Resource Distillation",
  "title_text": "Conditional Error Exponents of Probabilistic Quantum Resource Distillation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:06Z",
  "url": "https://research.draconitic.com/paper/4ms28e7mcge8g",
  "venue": "arXiv",
  "versions": []
}