Year: 2026
Type: preprint
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 $\varepsilon$-far in trace distance from all Gaussian states, can be accomplished using the optimal number $Θ(\varepsilon^{-2})$ 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.
Source: arXiv (Cornell University)
Authors: West, Maxwell, Larocca, Martin
Institutions: Los Alamos National Laboratory, Quantum Science Center
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G450742849, G841638809
OpenAlex ID: W7216365744