Finite-Block-Length Analysis in Classical and Quantum Information Theory

TL;DR

This paper reviews finite-size effects in classical and quantum information theory, highlighting their importance in practical scenarios where system sizes are limited, and discusses implications for coding technology in real-world applications.

Contribution

It provides a comparative review of finite block-length analysis in both classical and quantum information theory, emphasizing practical relevance.

Findings

Finite-size effects significantly impact coding performance.

Quantum and classical finite block-length analyses share common challenges.

Applied aspects of finite-size effects are discussed in detail.

Abstract

Coding technology is used in several information processing tasks. In particular, when noise during transmission disturbs communications, coding technology is employed to protect the information. However, there are two types of coding technology: coding in classical information theory and coding in quantum information theory. Although the physical media used to transmit information ultimately obey quantum mechanics, we need to choose the type of coding depending on the kind of information device, classical or quantum, that is being used. In both branches of information theory, there are many elegant theoretical results under the ideal assumption that an infinitely large system is available. In a realistic situation, we need to account for finite size effects. The present paper reviews finite size effects in classical and quantum information theory with respect to various topics, including applied aspects.