Testing bosonic and fermionic Gaussian states with a constant number of copies
Abstract
Bosonic and fermionic Gaussian quantum states are families of quantum states that play a central role in quantum physics and quantum information processing. We study the problem of testing whether a given state is either Gaussian, or has bounded overlap with any Gaussian state. Previous analyses of this testing problem led to tests that require a number of copies of the state that scales with the number of modes (the system size). In this work we show that a constant number of copies of the state suffices. We derive these results based on the symmetries of identical copies of Gaussian states, and by bounding the distance to the set of Gaussian states through a gradient flow and a spectral bound studied previously for the Kac random walk on a sphere.
Related
- Optimal testing of fermionic and bosonic Gaussian states
- Entangled measurements are necessary for optimal tomography of mixed fermionic Gaussian states and of bosonic Gaussian states near the vacuum
- Exponential lower bounds on the fermionic Gaussian rank of magic states and the bosonic coherent state rank of Fock states
- Robust exponential lower bounds for fermionic and bosonic Gaussian ranks
- Improved classical optimization of fermionic Hamiltonians beyond Gaussian states
BibTeX
@misc{briet2026testing,
title = {{Testing bosonic and fermionic Gaussian states with a constant number of copies}},
author = {Jop Briët and Davi Castro-Silva and Michael Walter and Freek Witteveen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06794},
eprint = {2610.06794},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06794},
}
RIS
TY - UNPB
TI - Testing bosonic and fermionic Gaussian states with a constant number of copies
AU - Jop Briët
AU - Davi Castro-Silva
AU - Michael Walter
AU - Freek Witteveen
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06794
UR - https://arxiv.org/abs/2610.06794
AB - Bosonic and fermionic Gaussian quantum states are families of quantum states that play a central role in quantum physics and quantum information processing. We study the problem of testing whether a given state is either Gaussian, or has bounded overlap with any Gaussian state. Previous analyses of this testing problem led to tests that require a number of copies of the state that scales with the number of modes (the system size). In this work we show that a constant number of copies of the state suffices. We derive these results based on the symmetries of identical copies of Gaussian states, and by bounding the distance to the set of Gaussian states through a gradient flow and a spectral bound studied previously for the Kac random walk on a sphere.
ER -