QLunch: Milad Moazami Goodarzi

Speaker: Milad Moazami Goodarzi

Title: Optimal convergence rates in the Cushen-Hudson quantum central limit theorem

Abstract: The Cushen-Hudson quantum central limit theorem states that quantum convolutions of a centered quantum state with finite energy converge weakly to a Gaussian state with matching first moments and covariance matrix. Recently, stronger versions of this result have been established by providing convergence rates in various distance measures. In this talk, I will present a recent contribution that establishes optimal, mode-independent rates of convergence in trace distance and quantum relative entropy under minimal moment assumptions. This work is based on a collaboration with Salman Beigi and Hami Mehrabi.