Description
While learning theory provides a framework for inferring unknown models from data, quantum inference tasks, such as state discrimination and parameter estimation, face unique constraints imposed by statistical limits and the fundamental laws of quantum mechanics. A central challenge is determining how efficiently information can be extracted from limited quantum resources.
In this work, we address a fundamental continuous-variable learning problem involving a single bosonic mode. We aim to learn an unknown displacement distribution, characterized by its probability density, $p(x)$, and corresponding characteristic function, $\lambda_\beta$. Using $N$ independent uses of the displacement channel, our objective is to construct an estimator, $\hat{\lambda}_\beta$, that bounds the additive error to $\epsilon$ over the interval $\beta \leq \beta_0$ with high confidence, $1-\delta$. This formulation naturally captures the sample complexity required to learn an unknown continuous-variable process from measurement data.
To expose the fundamental limits of this problem, we recast it as a binary hypothesis testing task and compare the performance of vacuum and squeezed-vacuum probes. Crucially, we reveal an exponential separation in the displacement parameter, $\beta_0$, regarding the minimum number of samples required to reliably distinguish the hypotheses. Our results prove that substantial improvements in learning efficiency arise solely from the choice of a non-classical probe state. This establishes squeezing as a powerful, independent resource for quantum learning, demonstrating that significant quantum advantages are achievable even in single-mode settings without entanglement.
| I am the presenting author | Yes |
|---|