{
  "abstract": "We develop a time--frequency framework for lattice GKP codes in which ideal codewords are realized in the modulation space $M^\\infty$ and identified, through a vector-valued Zak transform, with a finite logical fibre over the continuous syndrome torus. Multi-window Gabor analysis then represents the logical vector by a finite block of adjoint-lattice coefficients. We prove that the normalized block map is an isometry, obtain an explicit recovering projection, and derive stable logical reconstruction. We further construct normalizable GKP approximants as lattice-envelope Gabor multipliers and establish weak-$*$ convergence and asymptotically isometric encoding. Finally, we recover displacement syndromes from phase relations between translated coefficient blocks and quantify their stability under additive perturbations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10802",
  "author_total": 2,
  "authors": [
    {
      "name": "Franz Luef"
    },
    {
      "name": "Eduard Ortega"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/97j6dp866f3xk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10802",
  "fulltext_url": null,
  "id": "97j6dp866f3xk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10802",
  "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",
      "cs.IT"
    ],
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      "arxiv",
      "math-ph"
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      "arxiv",
      "math.FA"
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      "arxiv",
      "math.IT"
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      "arxiv",
      "math.MP"
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      "arxiv",
      "math.OA"
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      "arxiv",
      "quant-ph"
    ],
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      "openalex",
      "2604|Mathematical Analysis and Transform Methods"
    ]
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  "openalex": "W7212255034",
  "pdf_url": "https://arxiv.org/pdf/2609.10802",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/97j6dp866f3xk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:48Z",
      "native_id": "2609.10802",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10802"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A Time-Frequency Framework for GKP Codes",
  "title_text": "A Time-Frequency Framework for GKP Codes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/97j6dp866f3xk",
  "venue": "arXiv",
  "versions": []
}