For almost every student of physics, the first course on quantum theory raises a lot of puzzling questions and creates a very uncertain picture of the quantum world.

This book presents a clear and detailed exposition of the fundamental concepts of quantum theory: states, effects, observables, channels and instruments. It introduces several up-to-date topics, such as state discrimination, quantum tomography, measurement disturbance and entanglement distillation. A separate chapter is devoted to quantum entanglement.

The theory is illustrated with numerous examples, reflecting recent developments in the field. The treatment emphasises quantum information, though its general approach makes it a useful resource for graduate students and researchers in all subfields of quantum theory. Focusing on mathematically precise formulations, the book summarises the relevant mathematics.

Table of Contents

1- Hilbert space refresher

2- Stat es and effects

3- Observables

4- Operations and channels

5- Measurement models and instruments

6- Entanglement

Review

"The authors are renowned experts in the field, and I find their presentation masterful..the authors present a thorough and well-structured treatise on the mathematical language of quantum theory. I can recommend it to any graduate student with some experience in quantum computing who is interested in the foundations of the subject."

Thomas Peters in Contemporary Physics

"In summary, this is a fine book that will serve well theoretical quantum physicists wishing to acquire essential mathematical tools and deepen their insight into the mathematical foundations of quantum theory;"

Paul Busch, Mathematical Reviews

Book Description

A clear and detailed exposition of the fundamental concepts of quantum theory for graduate students and researchers.

About the Author

Teiko Heinosaari is a researcher at the Turku Centre for Quantum Physics, Finland. His research focuses on quantum measurements and quantum information theory.

Mário Ziman is a researcher at the Research Center for Quantum Information, the Institute of Physics at the Slovak Academy of Sciences, Bratislava and lectures at the Faculty of Informatics, Masaryk University, Brno. His research interests include foundations of quantum physics, quantum estimations and quantum information theory.