Abstract

One of the fundamental problems in information theory is to clarify the trade-offs between the performance of an information task, the size of the coding strategy, and the coding rate that determines the efficiency of the task. Error exponent analysis was proposed as a powerful methodology to study how rapidly the error probability of the task exponentially decays with an increase of coding length provided a fixed rate. This talk will present an exposition on error exponent analysis in quantum Shannon theory. In particular, we study two important quantum information processing protocols – classical data compression with quantum side information, and classical communications over quantum channels, and establish tight bounds for the error probability in the finite coding blocklength regime. Finally, we discuss the open problems along this line of research.