{
  "abstract": "A quantum state is called flat if it is proportional to a projector. There has been recent interest in studying antiflatness, the property of diverging from flat states, and establishing a resource theory for it. Identifying the free operations (the Flatness-Preserving Operations (FPOs)) remained an open problem. For this purpose, we first discuss Orthogonality-Preserving Operations (OPOs), of which trivial examples are unitary operations in an isolated system. More generally, we give a simple proof that all OPOs are isometric embeddings consisting of combinations of unitaries/isometries and appending a fixed state. We then show that all FPOs are either constant maps to some fixed flat state or a special case of an OPO, where the appended fixed state must be a flat state. We also show that the only possible flat convex combinations of flat states are those of orthogonal flat states with weights given by their purities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30697",
  "author_total": 2,
  "authors": [
    {
      "name": "Otto Veltheim"
    },
    {
      "name": "Esko Keski-Vakkuri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bz6zb858c5rb2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30697",
  "fulltext_url": null,
  "id": "bz6zb858c5rb2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30697",
  "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 Information and Cryptography"
    ]
  ],
  "openalex": "W7204924897",
  "pdf_url": "https://arxiv.org/pdf/2608.30697",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bz6zb858c5rb2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.30697",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30697"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Flatness-Preserving Operations",
  "title_text": "Flatness-Preserving Operations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/bz6zb858c5rb2",
  "venue": "arXiv",
  "versions": []
}