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Quantum Information Processing with Finite Resources

Mathematical Foundations

  • Book
  • © 2016

Overview

Authors:
  1. Marco Tomamichel

    1. School of Physics, The University of Sydney School of Physics, Singapore, Singapore

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Part of the book series: SpringerBriefs in Mathematical Physics (BRIEFSMAPHY, volume 5)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    • Marco Tomamichel
    Pages 1-10

  3. Modeling Quantum Information

    • Marco Tomamichel
    Pages 11-32

  4. Norms and Metrics

    • Marco Tomamichel
    Pages 33-45

  5. Quantum Rényi Divergence

    • Marco Tomamichel
    Pages 47-72

  6. Conditional Rényi Entropy

    • Marco Tomamichel
    Pages 73-89

  7. Smooth Entropy Calculus

    • Marco Tomamichel
    Pages 91-114

  8. Selected Applications

    • Marco Tomamichel
    Pages 115-126

  9. Back Matter

    Pages 127-138
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Keywords

About this book

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 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.

 

Reviews

“Broadly speaking, this book studies finite resource quantum information theory. … A helpful table of notational conventions is given for easy reference. Norms and metrics for quantum states are discussed. … each chapter ends with background and references for further reading. This book is at a suitable level for graduate students or researchers in physics or mathematics, with a reasonably strong linear algebra background.” (Sarah Plosker, Mathematical Reviews, January, 2017)

Authors and Affiliations

  • School of Physics, The University of Sydney School of Physics, Singapore, Singapore

    Marco Tomamichel

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