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Quantum Measurement

  • Paul Busch
  • Pekka Lahti
  • Juha-Pekka Pellonpää
  • Kari Ylinen

Part of the Theoretical and Mathematical Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
    Pages 1-10
  3. Mathematics

    1. Front Matter
      Pages 11-11
    2. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 13-36
    3. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 37-62
    4. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 63-100
    5. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 101-126
    6. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 127-136
    7. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 137-162
    8. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 163-187
  4. Elements

    1. Front Matter
      Pages 189-189
    2. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 191-224
    3. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 225-260
    4. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 261-274
    5. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 275-285
    6. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 287-315
  5. Realisations

    1. Front Matter
      Pages 317-317
    2. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 319-343
    3. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 345-365
    4. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 367-388
    5. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 389-403
    6. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 405-424
    7. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 425-462
  6. Foundations

    1. Front Matter
      Pages 463-463
    2. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 465-476
    3. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 477-488
    4. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 489-497
    5. Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
      Pages 499-536
  7. Back Matter
    Pages 537-542

About this book

Introduction

This is a book about the Hilbert space formulation of quantum mechanics and its measurement theory. It contains a synopsis of what became of the Mathematical Foundations of Quantum Mechanics since von Neumann’s classic treatise with this title. Fundamental non-classical features of quantum mechanics—indeterminacy and incompatibility of observables, unavoidable measurement disturbance, entanglement, nonlocality—are explicated and analysed using the tools of operational quantum theory.

The book is divided into four parts: 1. Mathematics provides a systematic exposition of the Hilbert space and operator theoretic tools and relevant measure and integration theory leading to the Naimark and Stinespring dilation theorems; 2. Elements develops the basic concepts of quantum mechanics and measurement theory with a focus on the notion of approximate joint measurability; 3. Realisations offers in-depth studies of the fundamental observables of quantum mechanics and some of their measurement implementations; and 4. Foundations discusses a selection of foundational topics (quantum-classical contrast, Bell nonlocality, measurement limitations, measurement problem, operational axioms) from a measurement theoretic perspective.

The book is addressed to physicists, mathematicians and philosophers of physics with an interest in the mathematical and conceptual foundations of quantum physics, specifically from the perspective of measurement theory.

Keywords

Fréchet-Riesz theorem Hilbert-Schmidt operator class Riesz-Markov-Kakutani representation theorem Cayley transform Stone's theorem Dilation theory Fourier-Plancherel transform Measurement schemes Qubit states Arthurs-Kelly model Eight-port homodyne detection Mach-Zehnder interferometer Bell inequalities Yanase condition Wigner-Araki-Yanase theorem Quantum logic

Authors and affiliations

  • Paul Busch
    • 1
  • Pekka Lahti
    • 2
  • Juha-Pekka Pellonpää
    • 3
  • Kari Ylinen
    • 4
  1. 1.Department of Mathematics, York Centre for Quantum TechnologiesUniversity of YorkYorkUnited Kingdom
  2. 2.Department of Physics and Astronomy, Turku Centre for Quantum PhysicsUniversity of TurkuTurkuFinland
  3. 3.Department of Physics and Astronomy, Turku Centre for Quantum PhysicsUniversity of TurkuTurkuFinland
  4. 4.Department of Mathematics and StatisticsUniversity of TurkuTurkuFinland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-43389-9
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-43387-5
  • Online ISBN 978-3-319-43389-9
  • Series Print ISSN 1864-5879
  • Series Online ISSN 1864-5887
  • Buy this book on publisher's site