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Original approach to foundations of quantum mechanics via mathematical statistics, leading to substantial generalization of standard notion of quantum observable
Includes an introduction to the ‘non-commutative’ mathematical statistics, providing a methodological basis for quantitative study of quantum measurements
Systematic study of correspondence between classical and quantum observables based on the concepts of covariance and optimality
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.
Foreword to 2nd English edition.- Foreword to 2nd Russian edition.- Preface.- Chapters: I. Statistical Models.- II. Mathematics of Quantum Theory.- III. Symmetry Groups in Quantum Mechanics.- IV. Covariant Measurements and Optimality.- V. Gaussian States.- VI Unbiased Measurements.- Supplement – Statistical Structure of Quantum Theory and Hidden Variables.- References.