IQIM Postdoctoral and Graduate Student Seminar

Note this week's talk begins at 2 pm in 114 E. Bridge

Abstract: Bosonic quantum systems enable key quantum technologies in computation, communication, and sensing. Gaussian quantum 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. 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 ε trace distance with high probability. We prove a lower bound of Ω(n^3/ε^2) for Gaussian measurements, matching the best known upper bound up to doubly logarithmic energy dependence, and Ω(n^2/ε^2) for arbitrary measurements. We further show an upper bound of O(n^2/ε^2) up to log factors, given that the Gaussian state is promised to be either pure or passive. Interestingly, non-Gaussian measurements are provably required for optimal learning of passive Gaussian states. We also show the role of adaptive learning in achieving energy-independent sample complexity. As a technical ingredient, we characterize the connection and difference between learning Gaussian states and learning their Wigner distributions. Our results advance quantum learning theory in the bosonic regimes and have practical applications.

Refreshments will be available following the talk.