Probabilistic and Statistical Aspects of Quantum Theory

  • Alexander Holevo

Part of the Publications of the Scuola Normale Superiore book series (PSNS)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Alexander Holevo
    Pages 1-36
  3. Alexander Holevo
    Pages 37-83
  4. Alexander Holevo
    Pages 85-140
  5. Alexander Holevo
    Pages 141-186
  6. Alexander Holevo
    Pages 187-218
  7. Alexander Holevo
    Pages 219-264
  8. Alexander Holevo
    Pages 265-303
  9. Back Matter
    Pages 305-323

About this book


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.


mathematical statistics quantum mechanics

Authors and affiliations

  • Alexander Holevo
    • 1
  1. 1.Steklov Mathematical InstituteMoscow

Bibliographic information