{
  "abstract": "We study how symmetry affects quantum advantage in two-party communication complexity. For any partial function $f$ on length-$n$ strings over a fixed alphabet of size $q$, invariant under simultaneous coordinate permutations, we prove $R^{\\mathrm{pub}}(f)=O_q(t\\log(2+n/t))$, where $t=\\min\\{n,Q^{\\ast}(f)^2\\}$, $R^{\\mathrm{pub}}$ denotes public-coin randomized communication complexity, and $Q^{\\ast}$ denotes entanglement-assisted quantum communication complexity. This bound is tight for set disjointness and extends the binary-alphabet result of Guan et al. with a smaller logarithmic overhead. The exponent of the logarithmic factor cannot be reduced by any fixed positive amount: for every fixed $\\varepsilon\\in(0,1)$, there are binary permutation-invariant partial functions with quantum communication complexity $O_\\varepsilon(\\log\\log n)$ and randomized communication complexity $Ω_\\varepsilon((\\log n)^{1-\\varepsilon})$. We also characterize quantum communication complexity by a combinatorial parameter up to a logarithmic factor. Growing alphabets and graph symmetries admit exponential separations. For every fixed $\\varepsilon\\in(0,1)$, we exhibit permutation-invariant partial functions on length-$n$ strings over an $n$-symbol alphabet with quantum communication complexity $O_\\varepsilon(\\log n)$ and randomized communication complexity $Ω_\\varepsilon(n^{1-\\varepsilon})$. For graph-invariant partial functions on $v$-vertex graphs, we obtain $O_\\varepsilon(\\log v)$ quantum versus $Ω_\\varepsilon(v^{2-\\varepsilon})$ randomized communication complexity. All separation protocols require no prior entanglement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40116",
  "author_total": 2,
  "authors": [
    {
      "name": "Yunqi Huang"
    },
    {
      "name": "Zekun Ye"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7pw58g7fbwj9k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40116",
  "fulltext_url": null,
  "id": "7pw58g7fbwj9k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40116",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7215123251",
  "pdf_url": "https://arxiv.org/pdf/2609.40116",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7pw58g7fbwj9k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2609.40116",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40116"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Advantage of Permutation-Invariant Functions in Communication Complexity",
  "title_text": "Quantum Advantage of Permutation-Invariant Functions in Communication Complexity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/7pw58g7fbwj9k",
  "venue": "arXiv",
  "versions": []
}