Practical Tests and Witnesses of Fermionic non-Gaussianity
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Quantum Physics arXiv:2605.26218 (quant-ph) [Submitted on 25 May 2026] Title:Practical Tests and Witnesses of Fermionic non-Gaussianity Authors:Tobias Haug, Xhek Turkeshi, Piotr Sierant View a PDF of the paper titled Practical Tests and Witnesses of Fermionic non-Gaussianity, by Tobias Haug and 2 other authors View PDF HTML (experimental) Abstract:Detecting when a quantum state leaves the efficiently simulable fermionic Gaussian regime is a central task for benchmarking quantum devices and certifying fermionic magic resources. We develop practical tests and witnesses based on fermionic antiflatness (FAF), a covariance-matrix-based measure of non-Gaussianity. For $n$-qubit states, we estimate FAF using two complementary protocols: two-copy Bell measurements and a single-copy scheme based on commuting matchings of Majorana bilinears. These yield testers that distinguish pure Gaussian states from states $\epsilon$-far from the Gaussian set, using $O(n^2/\epsilon^2)$ two-copy Bell measurements or $O(n^3/\epsilon^4)$ single-copy measurements, improving the state of the art in the dependence on both $n$ and $\epsilon$. For mixed states, we introduce a purity-corrected FAF witness that certifies non-Gaussianity and is highly robust to noise. With our witness, we demonstrate on the IQM quantum computer that noise can both reduce and enhance non-Gaussianity. Finally, by examining pseudo non-Gaussianity, we show that the cryptographic task of pseudorandom-state generation requires extensive fermionic non-Gaussianity. Together, these results provide experimentally accessible tools for detecting, witnessing, and quantifying non-Gaussian fermionic resources. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2605.26218 [quant-ph] (or arXiv:2605.26218v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.26218 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Piotr Sierant [view email] [v1] Mon, 25 May 2026 18:00:03 UTC (326 KB) Full-text links: Access Paper: View a PDF of the paper titled Practical Tests and Witnesses of Fermionic non-Gaussianity, by Tobias Haug and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: cond-mat cond-mat.stat-mech References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)