TIMS Seminar in Advanced Science
Speaker: 鄭皓中 (Hao-Chung Cheng, NTU)
Title: A Novel Matrix Concentration Inequality and Error Exponent for Quantum Soft Covering
How well can we approximate a quantum channel output state using a codebook with a certain size? In this work, we study the so-called quantum soft covering problem, which is to use a random codebook to approximate the target output state of a quantum channel. We establish a one-shot exponential bound on the expected trace-norm distance between the codebook-induced state and the true state. When using an independently and identically distributed random codebook with a rate above the quantum mutual information, we prove that the trace distances decay exponentially with error exponents determined by the Legendre transform of the quantum sandwiched Rényi information. As a result, it implies a tight bound on the information leakage to Eavesdroppers in private communication over wiretap quantum channels.
Our proof technique is to establish a novel matrix concentration inequality by using interpolation of noncommutative $L_p$ space. This may have applications elsewhere.
This work is jointly collaborated with Li Gao at the University of Houston and can be found at https://arxiv.org/abs/2202.10995.
Dr. Hao-Chung Cheng is a scientist and engineer in the quantum information frontier. He is currently an Assistant Professor at the Department of Electrical Engineering, and the Graduate Institute of Communication Engineering, National Taiwan University (NTU). Dr. Cheng received his bachelor's degree in the Department of Electrical Engineering, NTU. He received his Ph.D. degrees at the Graduate Institute of Communication Engineering, NTU, and at the Centre for Quantum Software and Information, School of Software, University of Technology Sydney. After receiving his Ph.D. degrees, Dr. Cheng joined the Department of Applied Mathematics and Theoretical Physics, at the University of Cambridge as a Postdoctoral Research Associate, and he was also affiliated with Darwin College. His research and scientific interests include quantum information processing, quantum communication, quantum machine learning, statistical signal processing, and matrix analysis.