{
  "abstract": "Can entangled noise erase entanglement more efficiently than separable noise? Standard robustness restricts the added noise to separable states; generalized robustness allows any state. We prove that the two costs coincide for every two-qubit state and give an explicit full-rank qubit--qutrit state with a strict gap. Positivity under partial transpose (PPT) characterizes separability in both dimensions, so the boundary is not caused by a failure of the PPT criterion. Instead, product-vector geometry permits a rank-one bridge between the two-qubit dual optimizations and supplies a two-dimensional completely entangled subspace for the qubit--qutrit separation. Local isometric embeddings complete the finite-dimensional bipartite classification, also for any fixed multipartite cut. Combined with known three-qubit separation, the result classifies universal equality relative to full separability in all finite multipartite systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28367",
  "author_total": 5,
  "authors": [
    {
      "name": "Xiao-Ke Wang"
    },
    {
      "name": "Zi-Yuan Liu"
    },
    {
      "name": "Ming-Yang Li"
    },
    {
      "name": "Shengjun Wu"
    },
    {
      "name": "Zeng-Bing Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3cfct0tn1d0ra.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28367",
  "fulltext_url": null,
  "id": "3cfct0tn1d0ra",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28367",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7214241315",
  "pdf_url": "https://arxiv.org/pdf/2609.28367",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3cfct0tn1d0ra.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.28367",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28367"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "The Minimal Dimension of Entangled-Noise Advantage",
  "title_text": "The Minimal Dimension of Entangled-Noise Advantage",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:56Z",
  "url": "https://research.draconitic.com/paper/3cfct0tn1d0ra",
  "venue": "arXiv",
  "versions": []
}