We establish a generalized quantum asymptotic equipartition property (AEP) beyond the i.i.d. framework where the random samples are drawn from two sets of quantum states. In particular, under suitable assumptions on the sets, we prove that all operationally relevant divergences converge to the quantum relative entropy between the sets. More specifically, both the smoothed min- and max-relative entropy approach the regularized relative entropy between the sets. Notably, the asymptotic limit has explicit convergence guarantees and can be efficiently estimated through convex optimization programs, despite the regularization, provided that the sets have efficient descriptions.

报告人简介：Dr. Kun Fang is a tenure-track assistant professor in the School of Data Science at The Chinese University of Hong Kong, Shenzhen (CUHK-Shenzhen). Before joining CUHK-Shenzhen, he served as a senior researcher and tech lead at the Institute for Quantum Computing, Baidu, from 2020 to 2023. Prior to that, he worked as a postdoctoral researcher at the University of Cambridge and the University of Waterloo from 2018 to 2020. He earned his PhD in Quantum Information from the University of Technology Sydney in 2018 and obtained his Bachelor’s degree in Mathematics from Wuhan University in 2015.