{
  "abstract": "We study quantum-assisted balanced rendezvous on the $d$-dimensional hypercube in a one-step two-agent quantum-walk framework, where the two agents move the same Hamming distance and meet at a common midpoint. The key structure is a projective $t$-sphere resolution, which governs exact finite-dimensional quantum attainment. Its scalar analogue recovers the corresponding classical characterization. We characterize finite-dimensional quantum attainment of the no-signalling benchmark, construct quantum strategies from projective sphere resolutions, and establish a rigidity theorem for optimal finite-dimensional strategies. A marked difference appears between nearest-neighbor and higher-cardinality updates: quantum advantage can occur in the former, whereas in the latter the geometry of the relevant Hamming spheres rules out exact finite-dimensional attainment of the no-signalling value. Together, these results connect quantum-walk dynamics, Hamming-sphere geometry, and quantum rendezvous within the quantum Bernoulli noises (QBN) framework.",
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  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12949",
  "author_total": 1,
  "authors": [
    {
      "name": "Ce Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2j8s8g09kwezg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12949",
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  "id": "2j8s8g09kwezg",
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  "landing_url": "https://arxiv.org/abs/2610.12949",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "arxiv",
      "math-ph"
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      "1702|Quantum Computing Algorithms and Architecture"
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  "pdf_url": "https://arxiv.org/pdf/2610.12949",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2j8s8g09kwezg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:36Z",
      "native_id": "2610.12949",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12949"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum-assisted rendezvous on hypercubes: a quantum Bernoulli noise approach",
  "title_text": "Quantum-assisted rendezvous on hypercubes: a quantum Bernoulli noise approach",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/2j8s8g09kwezg",
  "venue": "arXiv",
  "versions": []
}