Quantum Information Processing with Finite Resources

Mathematical Foundations

  • Marco Tomamichel

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

Table of contents

  1. Front Matter
    Pages i-ix
  2. Marco Tomamichel
    Pages 1-10
  3. Marco Tomamichel
    Pages 11-32
  4. Marco Tomamichel
    Pages 33-45
  5. Marco Tomamichel
    Pages 47-72
  6. Marco Tomamichel
    Pages 73-89
  7. Marco Tomamichel
    Pages 91-114
  8. Marco Tomamichel
    Pages 115-126
  9. Back Matter
    Pages 127-138

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 investigation 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.


Entanglement Information Processing Quantum Channel Quantum Computers Quantum Cryptography Quantum Device Quantum Shannon Theory Renyi Divergence Renyi Entropy Smooth Entropy

Authors and affiliations

  • Marco Tomamichel
    • 1
  1. 1.School of PhysicsThe University of Sydney School of PhysicsSingaporeSingapore

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