An asymmetry lower bound on fermionic non-Gaussianity
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arXiv
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| Format: | Preprint |
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2026
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| author | Ares, Filiberto Mazzoni, Michele Murciano, Sara Szász-Schagrin, Dávid Calabrese, Pasquale Piroli, Lorenzo |
| author_facet | Ares, Filiberto Mazzoni, Michele Murciano, Sara Szász-Schagrin, Dávid Calabrese, Pasquale Piroli, Lorenzo |
| contents | Fermionic Gaussian states are a fundamental tool in many-body physics, faithfully representing non-interacting quantum systems and allowing for efficient numerical simulations. Given a many-body wave function, it is therefore interesting to ask how much it differs from that of a Gaussian state, as quantified by the notion of non-Gaussianity. In this work, we relate measures of non-Gaussianity with the Shannon entropy of the particle-number distribution, coinciding with the particle-number asymmetry for pure states. We derive a lower bound on the relative entropy of non-Gaussianity in terms of the exponential of the Shannon entropy, and study numerically its tightness for large system sizes. Our bound is non-trivial for large values of the asymmetry and relies on the concentration of the particle-number distribution of (mixed) fermionic Gaussian states. Since the Shannon entropy of the particle-number distribution is often efficient to compute or experimentally measure, our results can be viewed as a practical way to lower bound non-Gaussianity, highlighting a non-trivial interplay with particle-number asymmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16762 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An asymmetry lower bound on fermionic non-Gaussianity Ares, Filiberto Mazzoni, Michele Murciano, Sara Szász-Schagrin, Dávid Calabrese, Pasquale Piroli, Lorenzo Quantum Physics Statistical Mechanics Mathematical Physics Fermionic Gaussian states are a fundamental tool in many-body physics, faithfully representing non-interacting quantum systems and allowing for efficient numerical simulations. Given a many-body wave function, it is therefore interesting to ask how much it differs from that of a Gaussian state, as quantified by the notion of non-Gaussianity. In this work, we relate measures of non-Gaussianity with the Shannon entropy of the particle-number distribution, coinciding with the particle-number asymmetry for pure states. We derive a lower bound on the relative entropy of non-Gaussianity in terms of the exponential of the Shannon entropy, and study numerically its tightness for large system sizes. Our bound is non-trivial for large values of the asymmetry and relies on the concentration of the particle-number distribution of (mixed) fermionic Gaussian states. Since the Shannon entropy of the particle-number distribution is often efficient to compute or experimentally measure, our results can be viewed as a practical way to lower bound non-Gaussianity, highlighting a non-trivial interplay with particle-number asymmetry. |
| title | An asymmetry lower bound on fermionic non-Gaussianity |
| topic | Quantum Physics Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2603.16762 |