In this talk is based on arXiv:2202.10263 and arXiv:2202.11590.
We establish a one-shot strong converse bound for privacy amplification against quantum side information using trace distance as a security criterion. This strong converse bound implies that in the independent and identical scenario, the trace distance exponentially converges to one in every finite blocklength when the rate of the extracted randomness exceeds the quantum conditional entropy. The established one-shot bound has an application to bounding the information leakage of classical-quantum wiretap channel coding and private communication over quantum channels. That is, the trace distance between Alice and Eavesdropper's joint state and its decoupled state vanishes as the rate of randomness used in hashing exceeds the quantum mutual information. On the other hand, the trace distance converges to one when the rate is below the quantum mutual information, resulting in an exponential strong converse. Our result also leads to an exponential strong converse for entropy accumulation, which complements a recent result by Dupuis [arXiv:2105.05342]. Lastly, our result and its applications apply to both the small deviation and moderate deviation regime. Namely, we obtain the optimal second-order rate when the trace distance is fixed or vanishing at sub-exponential speed.
Dr. Hao-Chung Cheng is a scientist and engineer in the quantum 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, University of Cambridge as a Postdoctoral Research Associate, and he also affiliated with the Darwin College. His research and scientific interests include quantum information processing, quantum communication, quantum machine learning, communication engineering, statistical signal processing, and matrix analysis.