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Qudit stabilizers beyond the free case and the twisted Kitaev model — arXiv:2603.29896

Source: arXiv (en)
Original: https://arxiv.org/abs/2603.29896
License (as archived): CC0-1.0
Archived: 2026-10-15T17:18:36.005Z
SHA-256 of the archived text: 14cf23df060a8653e307bf47ecf483391f7b77129df33a3cc50fa39efe7b5fb0
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How to cite

Qudit stabilizers beyond the free case and the twisted Kitaev model — arXiv:2603.29896 — arXiv (en), https://arxiv.org/abs/2603.29896 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_7c8a4e1680f2 (Metraipolis archive dc_7c8a4e1680f2, sha256 14cf23df060a8653e307bf47ecf483391f7b77129df33a3cc50fa39efe7b5fb0)

BibTeX

@misc{dc7c8a4e1680f2,
  title = {Qudit stabilizers beyond the free case and the twisted Kitaev model — arXiv:2603.29896},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2603.29896},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_7c8a4e1680f2; sha256 14cf23df060a8653e307bf47ecf483391f7b77129df33a3cc50fa39efe7b5fb0},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2603.29896. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study the stabiliser formalism for qudits of arbitrary dimension $d$. In the free case, we show that the basic theorem of the stabiliser formalism remains valid: if the stabiliser subgroup $H$ is free as a $Z/dZ$-module and contains no non-trivial scalars, then the protected space $V^H$ is naturally identified with the state space of a smaller number of qudits of the same dimension, and the quotient $N(H)/H$ is identified with the Pauli group on a smaller number of qudits. We then remove the freeness assumption and describe the resulting structure in general. In this case, the protected space is identified with a tensor product of qudit spaces of possibly smaller dimensions, and the quotient $N(H)/H$ is described by a corresponding product of qudit Pauli groups, possibly of smaller dimensions, over a common center. We also characterise the shifted free case, which is exactly the situation in which $N(H)/H$ is again an ordinary qudit Pauli group. Our approach is algebraic and uniform, and applies in particular to the qudit Kitaev model and to its shifted and twisted variants.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-17 in quant-ph).
Categorie arXiv: Quantum Algebra (math.QA) ; Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2603.29896 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-15T16:20:45.900Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-09-17?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).