Non-Gaussianity of random quantum states
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910234669219840 |
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| author | Ares, Filiberto Murciano, Sara Calabrese, Pasquale |
| author_facet | Ares, Filiberto Murciano, Sara Calabrese, Pasquale |
| contents | We study the fermionic non-Gaussianity in typical quantum states, focusing on Haar random states of qubits with or without a global $U(1)$ symmetry. Using the Weingarten calculus, we derive analytical predictions for the non-Gaussianity, defined as the relative entropy between the reduced density matrix and its Gaussianized counterpart. We identify two regimes controlled by the ratio between the subsystem and the system size, $\ell/L$. For $\ell/L < 1/2$, the non-Gaussianity vanishes in the absence of symmetries, because typical reduced density matrices are exponentially close to the maximally mixed state. In the presence of a global $U(1)$ symmetry, instead, it remains small but finite. By contrast, in the regime $\ell/L > 1/2$, the non-Gaussianity becomes extensive. These results establish the typical scaling of fermionic non-Gaussianity in random states and analyze how this is modified by the presence of global symmetries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18986 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-Gaussianity of random quantum states Ares, Filiberto Murciano, Sara Calabrese, Pasquale Statistical Mechanics Quantum Physics We study the fermionic non-Gaussianity in typical quantum states, focusing on Haar random states of qubits with or without a global $U(1)$ symmetry. Using the Weingarten calculus, we derive analytical predictions for the non-Gaussianity, defined as the relative entropy between the reduced density matrix and its Gaussianized counterpart. We identify two regimes controlled by the ratio between the subsystem and the system size, $\ell/L$. For $\ell/L < 1/2$, the non-Gaussianity vanishes in the absence of symmetries, because typical reduced density matrices are exponentially close to the maximally mixed state. In the presence of a global $U(1)$ symmetry, instead, it remains small but finite. By contrast, in the regime $\ell/L > 1/2$, the non-Gaussianity becomes extensive. These results establish the typical scaling of fermionic non-Gaussianity in random states and analyze how this is modified by the presence of global symmetries. |
| title | Non-Gaussianity of random quantum states |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2605.18986 |