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Robustness of Magic and the Directed Geometry of State Conversion — arXiv:2610.38401

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.38401
License (as archived): CC0-1.0
Archived: 2026-11-03T08:19:52.587Z
SHA-256 of the archived text: f2d15408140366d07960490414a53ec53275f0269092988011a8817991015d69
Stable URL of this page: https://metraipolis.com/documento/dc_ea0eb65791ef

How to cite

Robustness of Magic and the Directed Geometry of State Conversion — arXiv:2610.38401 — arXiv (en), https://arxiv.org/abs/2610.38401 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_ea0eb65791ef (Metraipolis archive dc_ea0eb65791ef, sha256 f2d15408140366d07960490414a53ec53275f0269092988011a8817991015d69)

BibTeX

@misc{dcea0eb65791ef,
  title = {Robustness of Magic and the Directed Geometry of State Conversion — arXiv:2610.38401},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.38401},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_ea0eb65791ef; sha256 f2d15408140366d07960490414a53ec53275f0269092988011a8817991015d69},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.38401. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.IT, nuovi lavori del giorno).
Categorie arXiv: Quantum Physics (quant-ph) ; Information Theory (cs.IT); Quantum Algebra (math.QA).
Pagina del lavoro: https://arxiv.org/abs/2610.38401 — 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 2026-11-03T08:05:38.789Z dalla pagina https://arxiv.org/list/math.IT/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).