{
  "abstract": "A multiset of pure quantum states is said to be k-learnable if there is a measurement strategy that always narrows an unknown sample drawn from the list down to one of at most k candidates. The parameter k interpolates between distinguishability and antidistinguishability, and provides a unified framework for partial state identification. We prove two universal, and optimal, Gram-matrix criteria for k-learnability: a Frobenius-norm sufficient condition and an entrywise-$\\ell_1$ necessary condition. We apply them to derive explicit learnability and copy-complexity guarantees for several well-known sets of states including SIC-POVMs, mutually unbiased bases, and stabilizer states. We further apply our results to zero-error mutation detection problems such as anomaly detection and changepoint detection.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17411",
  "author_total": 4,
  "authors": [
    {
      "name": "Nathaniel Johnston"
    },
    {
      "name": "Benjamin Lovitz"
    },
    {
      "name": "Vincent Russo"
    },
    {
      "name": "Jamie Sikora"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7wh2hcje2gs5d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17411",
  "fulltext_url": null,
  "id": "7wh2hcje2gs5d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17411",
  "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": "W7213402343",
  "pdf_url": "https://arxiv.org/pdf/2609.17411",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7wh2hcje2gs5d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2609.17411",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17411"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Sharp bounds for perfect quantum state classification beyond antidistinguishability",
  "title_text": "Sharp bounds for perfect quantum state classification beyond antidistinguishability",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:41Z",
  "url": "https://research.draconitic.com/paper/7wh2hcje2gs5d",
  "venue": "arXiv",
  "versions": []
}