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Probabilistic and Statistical Aspects of Quantum Theory

  • Book
  • © 2011

Overview

Authors:
  1. Alexander Holevo

    1. Steklov Mathematical Institute, Moscow

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  • Original approach to foundations of quantum mechanics via mathematical statistics leading to substantial generalization of standard notion of quantum observable

  • Introduction to the “noncommutative” 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

Part of the book series: Publications of the Scuola Normale Superiore (PSNS, volume 1)

Part of the book sub series: Monographs (Scuola Normale Superiore) (MSNS)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Statistical models

    • Alexander Holevo
    Pages 1-36

  3. Mathematics of quantum theory

    • Alexander Holevo
    Pages 37-83

  4. Symmetry groups in quantum mechanics

    • Alexander Holevo
    Pages 85-140

  5. Covariant measurements and optimality

    • Alexander Holevo
    Pages 141-186

  6. Gaussian states

    • Alexander Holevo
    Pages 187-218

  7. Unbiased measurements

    • Alexander Holevo
    Pages 219-264

  8. Supplement

    • Alexander Holevo
    Pages 265-303

  9. Back Matter

    Pages 305-323
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Keywords

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.

Authors and Affiliations

  • Steklov Mathematical Institute, Moscow

    Alexander Holevo

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