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Perfect state transfer on mixed graphs: complete classes and transfer times — arXiv:2610.08333

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.08333
License (as archived): CC0-1.0
Archived: 2026-10-07T11:53:19.544Z
SHA-256 of the archived text: 714972f5841c32257a6699c44d82138b634d6aaec6bb43ed51811f27b8531088
Stable URL of this page: https://metraipolis.com/documento/dc_bdffdce2932d

How to cite

Perfect state transfer on mixed graphs: complete classes and transfer times — arXiv:2610.08333 — arXiv (en), https://arxiv.org/abs/2610.08333 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_bdffdce2932d (Metraipolis archive dc_bdffdce2932d, sha256 714972f5841c32257a6699c44d82138b634d6aaec6bb43ed51811f27b8531088)

BibTeX

@misc{dcbdffdce2932d,
  title = {Perfect state transfer on mixed graphs: complete classes and transfer times — arXiv:2610.08333},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.08333},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_bdffdce2932d; sha256 714972f5841c32257a6699c44d82138b634d6aaec6bb43ed51811f27b8531088},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.08333. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

For perfect state transfer (PST) on unweighted mixed graphs, we classify the normalized transfer times of complete PST classes. A finite set $\Lambda\subset\mathbb R/\mathbb Z$ containing zero occurs at a nonstationary periodic vertex if and only if $\cos(2\pi(x-y))\in\mathbb Q$ for all $x,y\in\Lambda$. Every admissible set has a connected oriented realization. We also classify the possible return phases of oriented realizations at the minimum vertex period. Transfers at rational multiples of the common minimum vertex period partition a complete class into sets of size at most six, or at most three in an oriented graph with return phase $-1$; both bounds are sharp. We construct complete classes of every finite size, including classes in which all transfers between distinct vertices occur at irrational multiples of the period and no switching automorphism maps a class vertex to a distinct class vertex. We also characterize simultaneous realization in connected oriented graphs with prescribed relative minimum vertex periods and return phases. The proof combines an imaginary quadratic field restriction with an unweighted construction that selects the complete target set.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Combinatorics (math.CO) ; Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2610.08333 — 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 2026-10-07T11:22:09.564Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).