Authors:
- Develops tools for a rigorous approach to central questions of quantum mechanics
- Clarifies some Key issues concerning the foundations and interpretation of quantum mechanics
- The extensive bibliography makes it a useful reference text for researchers
- Includes supplementary material: sn.pub/extras
Part of the book series: Theoretical and Mathematical Physics (TMP)
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Table of contents (23 chapters)
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Front Matter
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Mathematics
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Front Matter
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Realisations
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Front Matter
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About this book
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
Reviews
“The book is constructed as a series of theorems, proofs, propositions, lemmas and corollaries … . Each chapter throughout the book is supplemented by a detailed set of references for further reading. Consequently, this monograph will be very useful as a reference work. … this is a volume that is really intended for mathematicians.” (Stephen J. Blundell, Contemporary Physics, Vol. 58 (4), September, 2017)
Authors and Affiliations
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Department of Mathematics, York Centre for Quantum Technologies, University of York, York, United Kingdom
Paul Busch
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Department of Physics and Astronomy, Turku Centre for Quantum Physics, University of Turku, Turku, Finland
Pekka Lahti, Juha-Pekka Pellonpää
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Department of Mathematics and Statistics, University of Turku, Turku, Finland
Kari Ylinen
Bibliographic Information
Book Title: Quantum Measurement
Authors: Paul Busch, Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen
Series Title: Theoretical and Mathematical Physics
DOI: https://doi.org/10.1007/978-3-319-43389-9
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Hardcover ISBN: 978-3-319-43387-5Published: 30 August 2016
Softcover ISBN: 978-3-319-82809-1Published: 22 April 2018
eBook ISBN: 978-3-319-43389-9Published: 23 August 2016
Series ISSN: 1864-5879
Series E-ISSN: 1864-5887
Edition Number: 1
Number of Pages: XII, 542
Number of Illustrations: 5 b/w illustrations, 2 illustrations in colour
Topics: Quantum Physics, History and Philosophical Foundations of Physics, Mathematical Physics, Quantum Information Technology, Spintronics, Functional Analysis