{
  "abstract": "Squashed entanglement is an additive bipartite entanglement measure. For a state $ρ_{AB}$, it is defined as the infimum of all conditional mutual information $I(A:B\\mid E)$ evaluated on extensions $ρ_{ABE}$. It was unresolved whether there is a bound on the dimension of the conditioning system, $E$, needed for this optimization. We show that no such cardinality bound is possible. Explicitly, we find that the squashed entanglement for a partially dephased Bell pair on two qubits cannot be achieved for any finite dimensional extension $E$. A crucial ingredient of this proof is a direct sum step, which in a sense, symmetrizes two purifying systems while keeping the conditional mutual information unchanged and the coherence no worse.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14031",
  "author_total": 2,
  "authors": [
    {
      "name": "Rabsan Galib Ahmed"
    },
    {
      "name": "Graeme Smith"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/842d4bwywfrs2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14031",
  "fulltext_url": null,
  "id": "842d4bwywfrs2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14031",
  "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.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7213280557",
  "pdf_url": "https://arxiv.org/pdf/2609.14031",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/842d4bwywfrs2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14031",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14031"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "No cardinality bound for squashed entanglement",
  "title_text": "No cardinality bound for squashed entanglement",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/842d4bwywfrs2",
  "venue": "arXiv",
  "versions": []
}