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Get baby started early on understanding the cryptology technology
(and maybe grown-ups can learn something too!).
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 Renyi 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 Renyi
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.
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