Non-Gaussianity of random quantum states

• URL: http://arxiv.org/abs/2605.18986v1
• Date: Mon, 18 May 2026 18:05:19 GMT
• Title: Non-Gaussianity of random quantum states
• Abstract summary: 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.<n>We derive analytical predictions for the non-Gaussianity, defined as the relative entropy between the reduced density matrix and its Gaussianized counterpart.<n>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.
• Score: 0.2621730497733947
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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