Quantum physics of operations

Author: P. Busch / et al.
Publisher:
Publish Date: 1999-04-01
Features:
Fragment: Prologue
The theory of quantum mechanics on Hilbert space has been the basis of fruitful and deep research into virtually all branches of physics for nearly seventy years. There seems to be no instance of a conflict between theoretical predictions and experimental results. In view of this success, it is remarkable that a few conceptual problems have resisted any attempt at resolution even until now. Some of them became tractable once the probabilistic structure of quantum mechanics was properly appreciated in its full generality. Gleason's theorem and the introduction of the notion of an observable as a positive operator-valued (POV) measure were the crucial steps in this development. Interestingly, the latter discovery was made independently in a variety of rather disparate areas of quantum physics, motivations ranging from foundational interests to fairly practical needs. This wide scope of the concept of POV measure already demonstrates its status as an integral part of the basic structure of quantum mechanics. The traditional notion of observables as self-adjoint operators constitutes a special case, represented by projection operator-valued (PV, or spectral) measures. The incorporation of POV measures into the quantum vocabulary has not only opened up new ways of approaching long-standing theoretical puzzles but also given rise to an elaboration of quantum measurement theory into a conceptually sound and mathematically rigorous, powerful tool for analyzing physical experiments. The ensuing research activities have led to a variety of reviews and monographs dealing with such diverse topics as the probabilistic and statistical aspects of quantum theory, quantum estimation and detection, quantum theory of open systems, photon-counting theory, or quantum mechanics on phase space. Much of this work is done on a high technical level and has thus contributed to setting new standards of rigor for investigations in the foundations of quantum physics. At the same time, the POV measure approach to quantum observables has gradually induced a probabilistic reformulation of quantum theory that is conceptually simpler and closer to experimental practice than the traditional approach. The present book is a result of two intimately related lines of research effort that took place in the past decade. On the one hand, quantum measurement theory has found manifold successful applications leading to new insights in the analysis of fundamental experiments. On the other hand, considerable progress has been made in working out the operational conditions needed for associating POV measures with the properties of physical systems. Both developments have contributed to fully appreciating the relevance of quantum mechanics as a theory of individual objects. The need for such a realistic interpretation of quantum theory is strikingly evident in these days where one is witnessing worldwide activities in carrying out exciting experiments with single microsystems such as atoms, ions, neutrons, or photons—experiments which formerly could only be conceived as thought experiments. Our primary concern is twofold. First, we wish to demonstrate the amazing capabilities of the quantum formalism if applied in its full-fledged probabilistic form. The advantages of POV measures and of measurement theory, taken as tools of investigation into the quantum world, will be illustrated in several steps and on different levels of sophistication. Yet the notion of a POV measure must itself be subjected to a measurement-theoretical analysis in order to elucidate its physical meaning. Reference to this double role of the measurement theory is the ultimate purpose of the term 'operational' appearing in the book title. The understanding of POV measures as representing observable properties of a physical system will be based on a realistic, individual interpretation of quantum theory. According to this interpretation, quantum mechanics describes physical systems existing independently once they have been prepared or identified by observation. Evidence for the presence of a system may be ascertained by means of determining its real (or actual) properties; and using ideal measurements, this can be achieved without thereby changing the system in any way. In general, however, a property will be non-objective (or potential) and may be actualized through measurement. Such repeatable measurements can thus be used