This book is a comprehensive survey of most of the theoretical and experimental achievements in the field of quantum estimation of states and operations. Albeit still quite young, this field has already been recognized as a necessary tool for research in quantum optics and quantum information, beyond being a fascinating subject in its own right since it touches upon the conceptual foundations of quantum mechanics. The book consists of twelve extensive lectures that are essentially self-contained and modular, allowing combination of various chapters as a basis for advanced courses and seminars on theoretical or experimental aspects. The last two chapters, for instance, form a self-contained exposition on quantum discrimination problems. The book will benefit graduate students and newcomers to the field as a high-level but accessible textbook, lecturers in search for advanced course material and researchers wishing to consult a modern and authoritative source of reference.

Quantum-state estimation is an important field in quantum information theory that deals with the characterization of states of affairs for quantum sources. This book begins with background formalism in estimation theory to establish the necessary prerequisites. This basic understanding allows us to explore popular likelihood- and entropy-related estimation schemes that are suitable for an introductory survey on the subject. Discussions on practical aspects of quantum-state estimation ensue, with emphasis on the evaluation of tomographic performances for estimation schemes, experimental realizations of quantum measurements and detection of single-mode multi-photon sources. Finally, the concepts of phase-space distribution functions, which compatibly describe these multi-photon sources, are introduced to bridge the gap between discrete and continuous quantum degrees of freedom.This book is intended to serve as an instructive and self-contained medium for advanced undergraduate and postgraduate students to grasp the basics of quantum-state estimation. Any reader with a solid foundation in quantum mechanics, linear algebra and calculus would be able to follow the book comfortably.

In this thesis, the author explains the background of problems in quantum estimation, the necessary conditions required for estimation precision benchmarks that are applicable and meaningful for evaluating data in quantum information experiments, and provides examples of such benchmarks. The author develops mathematical methods in quantum estimation theory and analyzes the benchmarks in tests of Bell-type correlation and quantum tomography with those methods. Above all, a set of explicit formulae for evaluating the estimation precision in quantum tomography with finite data sets is derived, in contrast to the standard quantum estimation theory, which can deal only with infinite samples. This is the first result directly applicable to the evaluation of estimation errors in quantum tomography experiments, allowing experimentalists to guarantee estimation precision and verify quantitatively that their preparation is reliable.

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

The nonlocality phenomena exhibited by entangled quantum systems are certainly one of the most extraordinary aspects of quantum theory. This book discusses this phe nomenon according to several points of view, i.e., according to different interpretations of the mathematics of the quantum formalism. The several interpretations of the Copenhagen interpretation, the many worlds, the de Broglie-Bohm, quantum logics, the decohering by the environment approach and the histories approach interpretations are scrutinized and criticized in detail. Recent results on cryptography, quantum bit commitment, quantum erasers and teleportation are also presented and discussed. In preparing the book we benefited from discussions with many people, but we would like, in particular, to express our gratitude to Professor B. d'Espagnat for his useful comments and suggestions. We are grateful also to Ms. L. Gentry EI-Dash for the English revision, to Dr. 1. E. Maiorino for the production of the figures and a careful reading of the manuscript, and for the statI of Plenum for advice and for having produced a nice book. Finally, the authors thank FAPESP (contract no. I 99612657-0) for a grant making this book possible. A. A. ORIB AND W. A. RODRIGUES, JR.

Quantum information describes the new field which bridges quantum physics and information science. The quantum world allows for completely new architectures and protocols. While originally formulated in continuous quantum variables, the field worked almost exclusively with discrete variables, such as single photons and photon pairs. The renaissance of continuous variables came with European research consortia such as ACQUIRE (Advanced Coherent Quantum Information Research) in the late 1990s, and QUICOV (Quantum Information with Continuous Variables) from 2000OCo2003. The encouraging research results of QUICOV and the new conference series CVQIP (Continuous Variable Quantum Information Processing) triggered the idea for this book. This book presents the state of the art of quantum information with continuous quantum variables. The individual chapters discuss results achieved in QUICOV and presented at the first five CVQIP conferences from 2002OCo2006. Many world-leading scientists working on continuous variables outside Europe also contribute to the book.

Quantum statistical inference, a research field with deep roots in the foundations of both quantum physics and mathematical statistics, has made remarkable progress since 1990. In particular, its asymptotic theory has been developed during this period. However, there has hitherto been no book covering this remarkable progress after 1990; the famous textbooks by Holevo and Helstrom deal only with research results in the earlier stage (1960s-1970s).This book presents the important and recent results of quantum statistical inference. It focuses on the asymptotic theory, which is one of the central issues of mathematical statistics and had not been investigated in quantum statistical inference until the early 1980s. It contains outstanding papers after Holevo's textbook, some of which are of great importance but are not available now.The reader is expected to have only elementary mathematical knowledge, and therefore much of the content will be accessible to graduate students as well as research workers in related fields. Introductions to quantum statistical inference have been specially written for the book. Asymptotic Theory of Quantum Statistical Inference: Selected Papers will give the reader a new insight into physics and statistical inference.

Quantum Detection and Estimation Theory