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Quantum Information Processing with Finite Resources : Mathematical Foundations - Marco Tomamichel

Quantum Information Processing with Finite Resources

Mathematical Foundations

By: Marco Tomamichel

eText | 14 October 2015

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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 informationtheory 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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Non-FictionSciencePhysicsQuantum Physics & Quantum Mechanics & Quantum Field TheoryComputing & I.T.Computer ScienceMathematical Theory of ComputationComputer Programming & Software DevelopmentAlgorithms & Data StructuresMathematicsDatabasesReference, Information & Interdisciplinary Subjects
Research & InformationInformation theoryEngineering & TechnologyMechanical Engineering & MaterialsMaterials ScienceMaterials & States of Matter

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