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 book is an up-to-date introduction to the quantum theory of measurement. Although the main principles of the field were elaborated in the 1930s by Bohr, Schrödinger, Heisenberg, von Neuman, and Mandelstam, it was not until the 1980s that technology became sufficiently advanced to allow its application in real experiments. Quantum measurement is now central to many ultra-high technology developments, such as "squeezed light," single atom traps, and searches for gravitational radiation. It is also considered to have great promise for computer science and engineering, particularly for its applications in information processing and transfer. The book begins with a brief introduction to the relevant theory and goes on to discuss all aspects of the design of practical quantum measurement systems.

Recent experimental advances in the control of quantum superconducting circuits, nano-mechanical resonators and photonic crystals has meant that quantum measurement theory is now an indispensable part of the modelling and design of experimental technologies. This book, aimed at graduate students and researchers in physics, gives a thorough introduction to the basic theory of quantum measurement and many of its important modern applications. Measurement and control is explicitly treated in superconducting circuits and optical and opto-mechanical systems, and methods for deriving the Hamiltonians of superconducting circuits are introduced in detail. Further applications covered include feedback control, metrology, open systems and thermal environments, Maxwell's demon, and the quantum-to-classical transition.

Modern quantum measurement for graduate students and researchers in quantum information, quantum metrology, quantum control and related fields.

Quantum measurement (Le., a measurement which is sufficiently precise for quantum effects to be essential) was always one of the most impor tant points in quantum mechanics because it most evidently revealed the difference between quantum and classical physics. Now quantum measure ment is again under active investigation, first of all because of the practical necessity of dealing with highly precise and complicated measurements. The nature of quantum measurement has become understood much bet ter during this new period of activity, the understanding being expressed by the concept of decoherence. This term means a physical process lead ing from a pure quantum state (wave function) of the system prior to the measurement to its state after the measurement which includes classical elements. More concretely, decoherence occurs as a result of the entangle ment of the measured system with its environment and results in the loss of phase relations between components of the wave function of the measured system. Decoherence is essentially nothing else than quantum measurement, but considered from the point of view of its physical mechanism and resolved in time. The present book is devoted to the two concepts of quantum measure ment and decoherence and to their interrelation, especially in the context of continuous quantum measurement.

An introduction to the arrow of time and a new, related, theory of quantum measurement.

This course-based monograph introduces the reader to the theory of continuous measurements in quantum mechanics and provides some benchmark applications. The approach chosen, quantum trajectory theory, is based on the stochastic Schrödinger and master equations, which determine the evolution of the a-posteriori state of a continuously observed quantum system and give the distribution of the measurement output. The present introduction is restricted to finite-dimensional quantum systems and diffusive outputs. Two appendices introduce the tools of probability theory and quantum measurement theory which are needed for the theoretical developments in the first part of the book. First, the basic equations of quantum trajectory theory are introduced, with all their mathematical properties, starting from the existence and uniqueness of their solutions. This makes the text also suitable for other applications of the same stochastic differential equations in different fields such as simulations of master equations or dynamical reduction theories. In the next step the equivalence between the stochastic approach and the theory of continuous measurements is demonstrated. To conclude the theoretical exposition, the properties of the output of the continuous measurement are analyzed in detail. This is a stochastic process with its own distribution, and the reader will learn how to compute physical quantities such as its moments and its spectrum. In particular this last concept is introduced with clear and explicit reference to the measurement process. The two-level atom is used as the basic prototype to illustrate the theory in a concrete application. Quantum phenomena appearing in the spectrum of the fluorescence light, such as Mollow’s triplet structure, squeezing of the fluorescence light, and the linewidth narrowing, are presented. Last but not least, the theory of quantum continuous measurements is the natural starting point to develop a feedback control theory in continuous time for quantum systems. The two-level atom is again used to introduce and study an example of feedback based on the observed output.

This book is the first systematic treatment of measures on projection lattices of von Neumann algebras. It presents significant recent results in this field. One part is inspired by the Generalized Gleason Theorem on extending measures on the projection lattices of von Neumann algebras to linear functionals. Applications of this principle to various problems in quantum physics are considered (hidden variable problem, Wigner type theorems, decoherence functional, etc.). Another part of the monograph deals with a fascinating interplay of algebraic properties of the projection lattice with the continuity of measures (the analysis of Jauch-Piron states, independence conditions in quantum field theory, etc.). These results have no direct analogy in the standard measure and probability theory. On the theoretical physics side, they are instrumental in recovering technical assumptions of the axiomatics of quantum theories only by considering algebraic properties of finitely additive measures (states) on quantum propositions.

The forty-nine papers collected here illuminate the meaning of quantum theory as it is disclosed in the measurement process. Together with an introduction and a supplemental annotated bibliography, they discuss issues that make quantum theory, overarching principle of twentieth-century physics, appear to many to prefigure a new revolution in science. Originally published in 1983. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

The Quantum Measurement Problem (QMP) is a single resource for information on the QMP and it establishes a basis for research on what is arguably the most well-known and still-unresolved scientific problem: how does our observed world relate to the quantum? The book is suitable for both undergraduate level study on a selective basis as well as graduate level study and for use as a resource for research scientists interested in aspects of the QMP. There are many sections that can even be profitably read by the general public to appreciate the history and future importance of the QMP. Although many books are now available that adequately address Quantum Information, this is the first book offering a comparable treatment for the QMP. The QMP has a companion website, https: //theqmp.com, with video presentations and other resources. There are some in the physics community that view the QMP only as a problem that requires an interpretation while others view its solution as essential to complete our physical description of the world and enhance our ability to design experimental probes of its physical elements in terms of quantum physics. This book critically examines these two viewpoints and resolves this dichotomy in favor of the latter viewpoint. The problem is precisely defined in terms of experimental operations and the scientific requirements that a resolution would have to meet. It explains why the QMP is a physical problem that requires more than an interpretation for its resolution and why a solution could have profound implications for physics as well as other fields. In particular, it uses quantum information methods for a constructive demonstration that unitary Schrödinger processes can be experimentally distinguished from measurement processes using well-established techniques such as Bell measurements, which would establish that measurement is a non-unitary process. Neither Schrödinger's equation nor the measurement postulate is found to be sufficient to explain measurement. For the first time, The QMP offers a single resource that thoroughly assesses the strengths and weaknesses of the major approaches to the QMP. . The exposition in The QMP contains eight chapters, including problem sets, with dual tracks throughout the book that allow both those with a technical background in quantum physics or quantum information as well as less-technical readers to come up to speed on the QMP, depending on their interests and background. . Chapters 1 and 2 are an introductory-level presentation of wave-particle duality and unitary Schrödinger processes. Chapter 3 is a key chapter that uses quantum information methods for a constructive demonstration that unitary Schrödinger processes can be experimentally distinguished from measurement processes using well-established techniques such as Bell measurements, which would establish that measurement is a non-unitary process. Chapter 4 presents a detailed definition of the QMP in terms of experimental observations and uses the results of Chapter 3 to systematically evaluate the strength and weaknesses of all the major approaches to the QMP in the literature and determine which constitute physical theories as opposed to philosophical interpretations. Chapter 5 gives an uncensored historical perspective leading to the development of quantum physics from the viewpoint of those physical aspects which will ultimately form the elements of the QMP. Chapter 6 presents a unique discussion of the Scientific Method and how the use of scientific deduction within the approach of radical conservatism can most proficiently address problems of quantum foundations. Chapter 7 presents concepts and mathematical tools useful for further research developments of both closed and open system approaches to the QMP. Chapter 8 presents conclusions and the status of the QMP for moving forward.