Quantum Information Processing with Finite Resources: Mathematical FoundationsThis 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 selfcontained 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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Contents
1  
2 Modeling Quantum Information  11 
3 Norms and Metrics  33 
4 Quantum Rényi Divergence  46 
5 Conditional Rényi Entropy  73 
6 Smooth Entropy Calculus  91 
7 Selected Applications  115 
AppendixSome Fundamental Resultsin Matrix Analysis  127 
References  131 
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Quantum Information Processing with Finite Resources: Mathematical Foundations Marco Tomamichel No preview available  2015 