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 $\varepsilon$-far in trace distance from all Gaussian states, can be accomplished using the optimal number $\Theta(\varepsilon^{-2})$ 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.

arXiv:2610.02050 [quant-ph]

(or arXiv:2610.02050v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2610.02050 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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