The Mathematical Language of Quantum Theory
From Uncertainty to Entanglement

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.

Introduction; 1. Hilbert space refresher; 2. States and effects; 3. Observables; 4. Operations and channels; 5. Measurement models and instruments; 6. Entanglement; Bibliography; Index.

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.