Practical Tests and Witnesses of Fermionic non-Gaussianity

• URL: http://arxiv.org/abs/2605.26218v1
• Date: Mon, 25 May 2026 18:00:03 GMT
• Title: Practical Tests and Witnesses of Fermionic non-Gaussianity
• Abstract summary: We develop tests and witnesses based on fermionic antiflatness (FAF)<n>For $n$-qubit states, we estimate FAF using two complementary protocols: two-copy Bell measurements and a single-copy scheme.<n>For mixed states, we introduce a purity-corrected FAF witness that certifies non-Gaussianity and is highly robust to noise.
• Score: 0.34757790689654594
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $ε$-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.

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