Principles of Quantum Communication Theory: A Modern Approach

TL;DR

The work presents an information-theoretic treatment of quantum communication, unifying foundational concepts with modern one-shot to asymptotic analyses. It introduces a comprehensive toolkit of quantum entropies, distinguishability measures, and entanglement quantification to support a wide range of communication tasks. The book details protocols for entanglement-assisted classical communication, classical communication, entanglement distillation, quantum communication, secret key distillation, private communication, and their feedback-assisted variants, with rigorous capacity and rate results. This framework advances the understanding of quantum communication and points to practical implications for secure and efficient information transmission in quantum networks.

Abstract

This is a preliminary version of a book in progress on the theory of quantum communication. We adopt an information-theoretic perspective throughout and give a comprehensive account of fundamental results in quantum communication theory from the past decade (and earlier), with an emphasis on the modern one-shot-to-asymptotic approach that underlies much of today's state-of-the-art research in this field. In Part I, we cover mathematical preliminaries and provide a detailed study of quantum mechanics from an information-theoretic perspective. We also provide an extensive and thorough review of quantum entropies, and we devote an entire chapter to the study of entanglement measures. Equipped with these essential tools, in Part II we study classical communication (with and without entanglement assistance), entanglement distillation, quantum communication, secret key distillation, and private communication. In Part III, we cover the latest developments in feedback-assisted communication tasks, such as quantum and classical feedback-assisted communication, LOCC-assisted quantum communication, and secret key agreement.