{
  "abstract": "While the Bloch sphere provides a canonical geometric representation for qubits, its generalization to pure qudit states ($d>2$) is not unique. This representation can be extended following two different approaches: increasing the number of points, as in the Majorana representation, or using a single point but in a space of larger dimension, as in the generalized Bloch representation. In this work, we compare these representations of pure qudit states by finding explicit analytical relations between them. In particular, a general formula of the Bloch vector in terms of the Majorana points of a given state is provided. We also analyze some suitable extensions of these representations in the case of pure permutation-symmetric two- and three-qubit states, deriving the corresponding relation between them. These analytical results allow us to study, from a geometric point of view, quantum correlations of special classes of two-qubit states.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11868",
  "author_total": 1,
  "authors": [
    {
      "name": "Louis Hanotel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/29rqsphmvt6r6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11868",
  "fulltext_url": null,
  "id": "29rqsphmvt6r6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11868",
  "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",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7221191271",
  "pdf_url": "https://arxiv.org/pdf/2610.11868",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/29rqsphmvt6r6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.11868",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11868"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "From Majorana to Bloch: two ways to generalize the Bloch sphere representation",
  "title_text": "From Majorana to Bloch: two ways to generalize the Bloch sphere representation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:54Z",
  "url": "https://research.draconitic.com/paper/29rqsphmvt6r6",
  "venue": "arXiv",
  "versions": []
}