What resources are needed for optimal learning of bosonic Gaussian states?

תקציר מקורי באנגליתarXiv:2603.18136v2 Announce Type: replace-cross Abstract: Continuous-variable systems enable key quantum technologies in computation, communication, and sensing. Bosonic Gaussian states emerge naturally in various such applications, including gravitational-wave and dark-matter detection. A fundamental question is how to characterize an unknown bosonic Gaussian state from as few samples as possible. Despite decades-long exploration, the ultimate efficiency limit remains unclear. In this work, we study the necessary and sufficient number of copies to learn an $n$-mode Gaussian state, with energy less than $E$, to $\varepsilon$ trace distance with high probability. We prove a lower bound of $\Omega(n^3/\varepsilon^2)$ for Gaussian measurements, matching the best known upper bound up to doubly