Practical Tests and Witnesses of Fermionic non-Gaussianity
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| Format: | Preprint |
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2026
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| author | Haug, Tobias Turkeshi, Xhek Sierant, Piotr |
| author_facet | Haug, Tobias Turkeshi, Xhek Sierant, Piotr |
| contents | 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 $ε$-far from the Gaussian set, using $O(n^2/ε^2)$ two-copy Bell measurements or $O(n^3/ε^4)$ single-copy measurements, improving the state of the art in the dependence on both $n$ and $ε$. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_26218 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Practical Tests and Witnesses of Fermionic non-Gaussianity Haug, Tobias Turkeshi, Xhek Sierant, Piotr Quantum Physics Statistical Mechanics 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 $ε$-far from the Gaussian set, using $O(n^2/ε^2)$ two-copy Bell measurements or $O(n^3/ε^4)$ single-copy measurements, improving the state of the art in the dependence on both $n$ and $ε$. 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. |
| title | Practical Tests and Witnesses of Fermionic non-Gaussianity |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2605.26218 |