{
  "abstract": "We introduce a relation problem constructed from the Clauser--Horne--Shimony--Holt (CHSH) game, which we call the two-round one-dimensional CHSH problem. Its two-round structure ensures that the CHSH questions are supplied only after the relevant Pauli-frame data have been fixed, thereby ruling out a simple classical strategy that solves the corresponding problem perfectly when all inputs are supplied simultaneously. We construct a quantum circuit on $2N$ qubits that uses only adjacent two-qubit gates, has operational depth at most eight, and achieves the optimal quantum success probability of CHSH, which is strictly smaller than one. We prove that, for every fixed $0\\leqδ<(\\sqrt{2}-1)/4$, any randomized classical circuit with fixed wiring and bounded gate fan-in that achieves an average success probability of at least $(2+\\sqrt{2})/4-δ$ requires depth $Ω(\\log N)$ after the questions of the second round are supplied. This yields an unconditional separation even though the quantum circuit is restricted to a one-dimensional geometry, whereas the classical circuit has no geometric locality restriction. The result shows that perfect quantum success is not necessary for unconditional quantum advantage with shallow circuits.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21237",
  "author_total": 3,
  "authors": [
    {
      "name": "Yonghae Lee"
    },
    {
      "name": "Jeonghyeon Shin"
    },
    {
      "name": "Soojoon Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8bb6aqz08xwf3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21237",
  "fulltext_url": null,
  "id": "8bb6aqz08xwf3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21237",
  "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 Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7213940653",
  "pdf_url": "https://arxiv.org/pdf/2609.21237",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8bb6aqz08xwf3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.21237",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21237"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Unconditional quantum advantage from a two-round CHSH problem in one dimension",
  "title_text": "Unconditional quantum advantage from a two-round CHSH problem in one dimension",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:56Z",
  "url": "https://research.draconitic.com/paper/8bb6aqz08xwf3",
  "venue": "arXiv",
  "versions": []
}