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SpringerBriefs in Mathematical Physics

Quantum Information Processing with Finite Resources

Mathematical Foundations

Authors: Tomamichel, Marco

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  • ISBN 978-3-319-21891-5
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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 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.

 

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)


Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook 46,00 €
price for Spain (gross)
  • ISBN 978-3-319-21891-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 57,19 €
price for Spain (gross)
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Bibliographic Information

Bibliographic Information
Book Title
Quantum Information Processing with Finite Resources
Book Subtitle
Mathematical Foundations
Authors
Series Title
SpringerBriefs in Mathematical Physics
Series Volume
5
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-21891-5
DOI
10.1007/978-3-319-21891-5
Softcover ISBN
978-3-319-21890-8
Series ISSN
2197-1757
Edition Number
1
Number of Pages
IX, 138
Number of Illustrations
4 illustrations in colour
Topics

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