Probabilistic and Statistical Aspects of Quantum Theory

Probabilistic and Statistical Aspects of Quantum Theory (Publications of the Scuola Normale Superiore / Monographs (Scuola Normale Superiore))
This book is devoted to aspects of the foundations of quantum mechanics in which probabilistic and statistical concepts play an essential role. The main part of the book concerns the quantitative statistical theory of quantum measurement, based on the notion of positive operator-valued measures. During the past years there has been substantial progress in this direction, stimulated to a great extent by new applications such as Quantum Optics, Quantum Communication and high-precision experiments. The questions of statistical interpretation, quantum symmetries, theory of canonical commutation relations and Gaussian states, uncertainty relations as well as new fundamental bounds concerning the accuracy of quantum measurements, are discussed in this book in an accessible yet rigorous way. Compared to the first edition, there is a new Supplement devoted to the hidden variable issue. Comments and the bibliography have also been extended and updated.

Table of Contents

Chapter 1 Statistical models
Chapter 2 Mathematics of quantum theory
Chapter 3 Symmetry groups in quantum mechanics
Chapter 4 Covariant measurements and optimality
Chapter 5 Gaussian states
Chapter 6 Unbiased measurements
Supplement Statistical structure of quantum theory and hidden variables