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Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity — arXiv:2610.02075

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.02075
License (as archived): CC0-1.0
Archived: 2026-10-07T11:38:23.145Z
SHA-256 of the archived text: 72ebafc6bf575decba3d4a9b2c35fcb892f7d4dcb2c5a4edbc8f4da0990377a9
Stable URL of this page: https://metraipolis.com/documento/dc_100aeffb243e

How to cite

Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity — arXiv:2610.02075 — arXiv (en), https://arxiv.org/abs/2610.02075 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_100aeffb243e (Metraipolis archive dc_100aeffb243e, sha256 72ebafc6bf575decba3d4a9b2c35fcb892f7d4dcb2c5a4edbc8f4da0990377a9)

BibTeX

@misc{dc100aeffb243e,
  title = {Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity — arXiv:2610.02075},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.02075},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_100aeffb243e; sha256 72ebafc6bf575decba3d4a9b2c35fcb892f7d4dcb2c5a4edbc8f4da0990377a9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.02075. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Fermionic non-Gaussianity is a resource for universal quantum computation that can be generated by interactions in quantum many-body systems. Using the magic Rényi entropy (MRE) as a measure of non-Gaussianity, we derive its universal upper bound and Haar mean, proving that typical Haar-random states attain the maximal MRE density of $\ln(4/3)$ per Majorana in the large-system limit. We also show that the MRE can differ extensively between states with identical covariance matrices. To investigate how non-Gaussianity grows toward this maximal density, we evolve a Gaussian state in imaginary and real time under the Sachdev-Ye-Kitaev Hamiltonian. By varying the imaginary- and real-time durations, we identify a first-order transition marked by a kink in the MRE density and spontaneous breaking of the permutation symmetry among the four copies used to evaluate the MRE. This transition represents a qualitative change in the non-Gaussianity of the state that is not reflected in the thermal free energy.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-10-02 in quant-ph).
Categorie arXiv: Quantum Physics (quant-ph) ; Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el).
Pagina del lavoro: https://arxiv.org/abs/2610.02075 — 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 2026-10-07T11:19:01.741Z dalla pagina https://arxiv.org/catchup/quant-ph/2026-10-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).