This book provides the reader with the mathematical framework required
to fully explore the potential of small quantum information processing
devices. As decoherence will continue to limit their size, it is
essential to master the conceptual tools which make such investigations
possible.
A strong emphasis is given to information measures that are essential
for the study of devices of finite size, including Rényi entropies and
smooth entropies. The presentation is self-contained and includes
rigorous and concise proofs of the most important properties of these
measures. The first chapters will introduce the formalism of quantum
mechanics, with particular emphasis on norms and metrics for quantum
states. This is necessary to explore quantum generalizations of Rényi
divergence and conditional entropy, information measures that lie at the
core of information theory. The smooth entropy framework is discussed
next and provides a natural means to lift many arguments from
information theory to the quantum setting.
Finally selected applications of the theory to statistics and
cryptography are discussed.
The book is aimed at graduate students in Physics and Information
Theory. Mathematical fluency is necessary, but no prior knowledge of
quantum theory is required.