{
  "abstract": "We study zero-error communication and exact simulation of quantum channels assisted by quantum no-signalling correlations. For a channel with Kraus operator space $K$, we introduce a semidefinite programming parameter $Γ(K)$ that is exactly multiplicative under tensor products and upper-bounds $Θ_{\\rm NS}(K)$, where $\\log_2Θ_{\\rm NS}(K)=C_{0,\\rm NS}(K)$ and $C_{0,\\rm NS}(K)$ denotes the asymptotic quantum no-signalling-assisted zero-error capacity. Among known upper bounds on $Θ_{\\rm NS}$ given by semidefinite programs, $Γ$ is the tightest. We also prove that the previously introduced simulation lower bound $Σ^{-}(K)$ is exactly multiplicative and satisfies $Θ_{\\rm NS}(K)\\leqΓ(K)\\leqΣ^{-}(K)\\leqΓ(K)^2$. Using this multiplicativity, we show that neither $S_{0,\\rm NS}(K)=\\log_2Σ^{-}(K)$ nor its regularized extension $S_{0,\\rm NS}(K)=\\lim\\nolimits_{n\\to\\infty}n^{-1}\\log_2Σ^{-}(K^{\\otimes n})$ holds in general. This answers an open question about the asymptotic simulation cost $S_{0,\\rm NS}(K)$. For classical-quantum channels, we obtain sharp bounds. If $r$ is the effective output dimension, then $Θ_{\\rm NS}\\leqΓ\\leq(1+r^{1/2})Θ_{\\rm NS}/2$ and $Γ\\leqΣ^{-}\\leq(1+r^{1/2})Γ/2$. If $k$ is the minimum rank of the output support projections, then $Σ^{-}/Θ_{\\rm NS}\\leq[(1+r^{1/2})/(1+k^{1/2})]^2$, and this bound is sharp for every $1\\leq k\\leq r$. Thus, we obtain the sharp bound $S_{0,\\rm NS}-C_{0,\\rm NS}\\leq2\\log_2[(1+r^{1/2})/(1+k^{1/2})]$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21071",
  "author_total": 2,
  "authors": [
    {
      "name": "Xin Li"
    },
    {
      "name": "Yinan Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/18gb3nhftm67w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21071",
  "fulltext_url": null,
  "id": "18gb3nhftm67w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21071",
  "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",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7222492891",
  "pdf_url": "https://arxiv.org/pdf/2610.21071",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/18gb3nhftm67w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:50Z",
      "native_id": "2610.21071",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21071"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Multiplicative Semidefinite Programming Upper Bounds on Quantum No-Signalling-Assisted Zero-Error Capacity",
  "title_text": "Multiplicative Semidefinite Programming Upper Bounds on Quantum No-Signalling-Assisted Zero-Error Capacity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/18gb3nhftm67w",
  "venue": "arXiv",
  "versions": []
}