Fermionic Gaussianity can be tested with mode-independent sample-complexity
Abstract
Deciding whether an unknown quantum state either belongs to, or is far from, a given family of states is a natural question of quantum information theory. In many such cases, there is a natural 2-copy test which always accepts whenever the state indeed belongs to the target family; it is often much more difficult, however, to bound the probability of acceptance for states that are far from the family. Here we develop a simple new technique for upper bounding this probability for general families, and therefore upper bounding the sample-complexity of the decision problem itself. As a particularly striking example of this framework, we show that deciding whether an unknown pure n-mode state is fermionic Gaussian, or at least ε-far in trace distance from all Gaussian states, can be accomplished using the optimal number Θ(ε−2) of copies. Remarkably, our analysis applies to the well-known Bell sampling procedure for testing fermionic Gaussianity, which we therefore show to be optimal, even compared to protocols making arbitrary collective and adaptive measurements. As a second example, we show that the analogous decision problem for the family of Slater determinant states can also be solved with mode-independent sample-complexity.
Related
- Testing quantum Gaussianity with constant sample complexity
- Practical fermionic shadows enabled by improved sample-complexity bounds
- Computable fermionic non-Gaussianity from the covariance matrix
- Fermionic non-Gaussianity via computable measures and experimentally accessible bounds
- Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity
BibTeX
@misc{west2026fermionic,
title = {{Fermionic Gaussianity can be tested with mode-independent sample-complexity}},
author = {Maxwell West and Martin Larocca},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02050},
eprint = {2610.02050},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02050},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fermionic Gaussianity can be tested with mode-independent sample-complexity
AU - Maxwell West
AU - Martin Larocca
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02050
UR - https://arxiv.org/abs/2610.02050
AB - Deciding whether an unknown quantum state either belongs to, or is far from, a given family of states is a natural question of quantum information theory. In many such cases, there is a natural 2-copy test which always accepts whenever the state indeed belongs to the target family; it is often much more difficult, however, to bound the probability of acceptance for states that are far from the family. Here we develop a simple new technique for upper bounding this probability for general families, and therefore upper bounding the sample-complexity of the decision problem itself. As a particularly striking example of this framework, we show that deciding whether an unknown pure n-mode state is fermionic Gaussian, or at least ε-far in trace distance from all Gaussian states, can be accomplished using the optimal number Θ(ε^−2) of copies. Remarkably, our analysis applies to the well-known Bell sampling procedure for testing fermionic Gaussianity, which we therefore show to be optimal, even compared to protocols making arbitrary collective and adaptive measurements. As a second example, we show that the analogous decision problem for the family of Slater determinant states can also be solved with mode-independent sample-complexity.
ER -