Detecting quantum non-Gaussianity with a single quadrature
Abstract
Full reconstruction of quantum states from measurement samples is often a prohibitively complex task, both in terms of the experimental setup and the scaling of the sample size with the system. This motivates the relatively easier task of certifying application-specific quantities using measurements that are not tomographically complete, i.e. that provide only partial information about the state related to the application of interest. Here, we focus on simplifying the measurements needed to certify non-Gaussianity in bosonic systems, a resource related to quantum advantage in various information processing tasks. We show that the statistics of a single quadrature measurement, corresponding to standard homodyne detection in quantum optics, can witness arbitrary degrees of non-Gaussianity as quantified by stellar rank. Our results are based on a version of Hudson's theorem for wavefunctions, proved in a companion paper [arXiv:2507.23468], revealing that the zeros in a homodyne distribution are signatures of quantum non-Gaussianity and higher stellar ranks. The validity of our witnesses is supported by a technical result showing that sets of states with bounded energy and finite stellar rank are compact. We provide an analysis of sample complexity, noise robustness, and experimental prospects. Our work drastically simplifies the setup required to detect quantum non-Gaussianity in bosonic quantum states.
Related
- Energetics of non-Gaussianity in single mode cavities
- Non-Gaussianity of random quantum states
- Work statistics of sudden quantum quenches: A random matrix theory perspective on Gaussianity and its deviations
- Testing quantum Gaussianity with constant sample complexity
- Fermionic non-Gaussianity via Bell sampling: monotones and efficient quantum algorithms
BibTeX
@misc{wassner2026detecting,
title = {{Detecting quantum non-Gaussianity with a single quadrature}},
author = {Clara Wassner and Jack Davis and Sacha Cerf and Ulysse Chabaud and Francesco Arzani},
howpublished = {HAL},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2507.23005},
eprint = {2507.23005},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05732602v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Detecting quantum non-Gaussianity with a single quadrature
AU - Clara Wassner
AU - Jack Davis
AU - Sacha Cerf
AU - Ulysse Chabaud
AU - Francesco Arzani
PY - 2026
DA - 2026/09/01
PB - HAL
DO - 10.48550/arxiv.2507.23005
UR - https://hal.science/hal-05732602v1
AB - Full reconstruction of quantum states from measurement samples is often a prohibitively complex task, both in terms of the experimental setup and the scaling of the sample size with the system. This motivates the relatively easier task of certifying application-specific quantities using measurements that are not tomographically complete, i.e. that provide only partial information about the state related to the application of interest. Here, we focus on simplifying the measurements needed to certify non-Gaussianity in bosonic systems, a resource related to quantum advantage in various information processing tasks. We show that the statistics of a single quadrature measurement, corresponding to standard homodyne detection in quantum optics, can witness arbitrary degrees of non-Gaussianity as quantified by stellar rank. Our results are based on a version of Hudson's theorem for wavefunctions, proved in a companion paper [arXiv:2507.23468], revealing that the zeros in a homodyne distribution are signatures of quantum non-Gaussianity and higher stellar ranks. The validity of our witnesses is supported by a technical result showing that sets of states with bounded energy and finite stellar rank are compact. We provide an analysis of sample complexity, noise robustness, and experimental prospects. Our work drastically simplifies the setup required to detect quantum non-Gaussianity in bosonic quantum states.
ER -