EAN: 9783319218908

QUANTUM INFORMATION PROCESSING WITH FINITE RESO...

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.

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