Quantum Measurement and Control

Abstract

In the last two decades there has been an enormous progress in theexperimental investigation of single quantum systems. This progress covers fields such as quantumoptics, quantum computation, quantum cryptography, and quantummetrology, which are sometimes summarized as `quantum technologies'.A key issue there is entanglement,which can be considered as the characteristic feature of quantumtheory. As disparate as these various fields maybe, they all have todeal with a quantum mechanical treatment of the measurement processand, in particular, the control process. Quantum control is, accordingto the authors, `control for which the design requires knowledge ofquantum mechanics'. Quantum control situations in which measurements occurat important steps are called feedback (or feedforward) control ofquantum systems and play a central role here.This book presents a comprehensive and accessible treatment of the theoreticaltools that are needed to cope with these situations. It also providesthe reader with the necessary background information about the experimentaldevelopments. The authors are both experts in this field to which theyhave made significant contributions. After an introduction to quantum measurement theory and a chapter onquantum parameter estimation, the central topic of open quantumsystems is treated at some length. This chapter includes a derivationof master equations, the discussion of the Lindblad form, anddecoherence – the irreversible emergence of classical propertiesthrough interaction with the environment. A separate chapter isdevoted to the description of open systems by the method of quantumtrajectories. Two chapters then deal with the central topic of quantumfeedback control, while the last chapter gives a concise introductionto one of the central applications – quantum information. Allsections contain a bunch of exercises which serve as a useful tool inlearning the material. Especially helpful are also various separateboxes presenting important background material on topics such asthe block representation or the feedback gain-bandwidth relation. Thetwo appendices on quantum mechanics and phase-space and on stochasticdifferential equations serve the same purpose.As the authors emphasize, the book is aimed at physicists as well ascontrol engineers who are already familiar with quantum mechanics. Ittakes an operational approach and presents all the material thatis needed to follow research on quantum technologies. On the other hand, conceptual issues such as the relevance of the measurement process for theinterpretation of quantum theory are neglected. Readers interested inthem may wish to consult instead a textbook such as Decoherence andthe Quantum-to-Classical Transition by Maximilian Schlosshauer.Although the present book does not contain applications to gravity, part of itscontent might become relevant for the physics of gravitational-wave detectionand quantum gravity phenomenology. In this respect it should be ofinterest also for the readers of this journal.