Non-Gaussianity of random quantum states
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, ℓ/L. For ℓ/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 ℓ/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.
Versions
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BibTeX
@misc{ares2026nongaussianity,
title = {{Non-Gaussianity of random quantum states}},
author = {Filiberto Ares and Sara Murciano and Pasquale Calabrese},
howpublished = {arXiv},
year = {2026},
month = may,
doi = {10.48550/arxiv.2605.18986},
eprint = {2605.18986},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.18986},
}
RIS
TY - UNPB
TI - Non-Gaussianity of random quantum states
AU - Filiberto Ares
AU - Sara Murciano
AU - Pasquale Calabrese
PY - 2026
DA - 2026/05/18
PB - arXiv
DO - 10.48550/arxiv.2605.18986
UR - https://arxiv.org/abs/2605.18986
AB - 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, ℓ/L. For ℓ/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 ℓ/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.
ER -