{
  "abstract": "In this work, we introduce a state-space distance calibrated by stabilizer states based on the dual structure of the robustness of magic (RoM), and show that RoM is exactly represented as the distance to the free-state set. We then extend this geometry to state conversion by defining the directed conversion deficiency $C_{\\mathcal F}$ as the distance between a target state and the set of states freely reachable from a given input state. The quantity $C_{\\mathcal F}$ characterizes free convertibility and is related to the minimum stabilizer quasiprobability weight required to represent the conversion residual through the relation $1+2C_{\\mathcal F}$. It also contains the conventional magic state resource lower bounds based on RoM and can detect stronger conversion obstructions. For single-qubit systems, we analytically construct a continuous family of mixed states with identical RoM but asymmetric convertibility.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38401",
  "author_total": 2,
  "authors": [
    {
      "name": "Satoshi Kanno"
    },
    {
      "name": "Yoshi-aki Shimada"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ma9evjdmy0s3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38401",
  "fulltext_url": null,
  "id": "2ma9evjdmy0s3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38401",
  "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"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38401",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ma9evjdmy0s3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.38401",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38401"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Robustness of Magic and the Directed Geometry of State Conversion",
  "title_text": "Robustness of Magic and the Directed Geometry of State Conversion",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/2ma9evjdmy0s3",
  "venue": "arXiv",
  "versions": []
}