From Classical to Quantum Shannon Theory by Mark M. Wilde
Abstract:
The aim of this book is to develop “from the ground up” many of the major, exciting, pre- and post-millenium developments in the general area of study known as quantum Shannon theory. As such, we spend a significant amount of time on quantum mechanics for quantum information theory (Part II), we give a careful study of the important unit protocols of teleportation, super-dense coding, and entanglement distribution (Part III), and we develop many of the tools necessary for understanding information transmission or compression (Part IV). Parts V and VI are the culmination of this book, where all of the tools developed come into play for understanding many of the important results in quantum Shannon theory.
From Chapter 1:
You may be wondering, what is quantum Shannon theory and why do we name this area of study as such? In short, quantum Shannon theory is the study of the ultimate capability of noisy physical systems, governed by the laws of quantum mechanics, to preserve information and correlations. Quantum information theorists have chosen the name quantum Shannon theory to honor Claude Shannon, who single-handedly founded the fi eld of classical information theory, with a groundbreaking 1948 paper [222]. In particular, the name refers to the asymptotic theory of quantum information, which is the main topic of study in this book. Information theorists since Shannon have dubbed him the “Einstein of the information age.”1 The name quantum Shannon theory is fit to capture this area of study because we use quantum versions of Shannon’s ideas to prove some of the main theorems in quantum Shannon theory.
This is of immediate importance if you are interested in current research in information theory. Of near-term importance if you are interested in practical design of algorithms for quantum information systems.