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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.
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.
The theory of quantum mechanical measuring process has been a
subject of increasing research interest during recent years. The
revival of interest in it was encouraged during the 1980's due to
the advances on the formal and conceptual structures of quantum
mechanics, accompanied with new experimental possibilities and
technological demands, as well as due to new ideas on the
interpretation of the theory. This proceedings is devoted to
reviewing the present situation on quantum measurement theory and
discussing the related philosophical implications.
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