{
  "abstract": "The construction of multiqubit unextendible product bases (UPBs) has been a long-standing problem. We give a systematic construction of multiqubit UPBs by studying their unextendible orthogonal matrices (UOMs) with graph-theoretic methods. Row decompositions of small UOMs produce the main intervals. Com- pletion graphs settle the remaining small UPB sizes, except for one size obtained from a good column structure. Nonexistence of the other UPB sizes follows from counts of fibres and row pairs. The computer is used only for a few finite UOM checks, whose exact tests are stated in the certificate appendix. These arguments determine the complete multiqubit UPB size spectrum in every dimension.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14788",
  "author_total": 2,
  "authors": [
    {
      "name": "Caohan Cheng"
    },
    {
      "name": "Lin Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cjawtp3ymwsnn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14788",
  "fulltext_url": null,
  "id": "cjawtp3ymwsnn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14788",
  "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": "W7213256531",
  "pdf_url": "https://arxiv.org/pdf/2609.14788",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cjawtp3ymwsnn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14788",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14788"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Systematic construction of multiqubit unextendible product bases",
  "title_text": "Systematic construction of multiqubit unextendible product bases",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/cjawtp3ymwsnn",
  "venue": "arXiv",
  "versions": []
}