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## Quantum Detection and Estimation Theory

Quantum Detection and Estimation Theory
## Quantum Detection and Estimation Theory

## Chemistry, Quantum Mechanics and Reductionism

The purpose of this book is to provide a deeper insight into the modern theories of molecular matter. It incorporates the most important developments which have taken place during the last decades and reflects the modern trend to abstraction. At the present state of the art we have acquired a fairly good knowledge of "how to. compute" small molecules us ing the methods of quantum chemistry. Yet, in spite of many statements to the contrary and many superficial discussions, the theoretical basis of chemistry and biology is not safely in our hands. It is all but impossible to summarize the modern developments of the theory of matter in nontechnical language. But I hope that I can give some feeling for the problems, the intellectual excitements and the wor ries of some theoreticians. I know very well that such an enterprise is a dangerous adventure and that one says that a clever scientist should take care of his reputation by barricading himself behind the safe wall of his speciality. This volume is not meant to be a textbook; in many respects it has complementary goals. For good and bad reasons, most textbooks ignore the historical and philosophical aspects and go ahead on the basis of crude simplifications; many even lie like the devil and do not shrink from naive indoctrination. Some sections of this book can be read as commentaries on our standard texts, they are intended to stir the waters with controversy.
## Introduction to Quantum-State Estimation

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. Contents:PrefaceAcknowledgmentsAcronymsSymbols and NotationsPreliminaries of Quantum-State EstimationInformationally Complete EstimationInformationally Incomplete EstimationPractical Aspects of State EstimationQuasi-Probability Distributions Readership: Advanced undergraduate and graduate students as well as researchers interested in quantum information, estimation theory, and quantum optics. Key Features:This is a relatively new topic with a paucity of literature in the marketThis book is a set of lecture notes that is more suitable for graduate-module teaching, covering the necessary basic elements of this subject in a pedagogical manner before introducing more advanced notions in the later chaptersA solution manual for the problems in the book is currently in the worksKeywords:Quantum State Estimation;Tomography;Quasi-Probability;Likelihood;Entropy;Constrained OptimizationReview: "This book is a detailed, well-written introduction to the way of inferring quantum states parameters from measurement data. This book is surely something to recommend to one's students." Dmitri Mogilevtsev Institute of Physics Minsk, Belarus
## Asymptotic Theory of Quantum Statistical Inference

' 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. Contents:Hypothesis TestingQuantum Cramér-Rao Bound in Mixed States ModelQuantum Cramér-Rao Bound in Pure States ModelGroup Symmetric Approach to Pure States ModelLarge Deviation Theory in Quantum EstimationFuther Topics on Quantum Statistical Inference Readership: Graduate students in quantum physics, mathematical physics, and probability and statistics. Keywords:Quantum Information;Estimation Theory;Statistics;Statistical Inference;Mathematical Physics;Asymptotic Theory;Hypothesis TestingReviews:“This book will give the scholars new insight into physics and statistical inference.”Zentralblatt MATH '
## Quantum Information Theory

A self-contained, graduate-level textbook that develops from scratch classical results as well as advances of the past decade.
## Compendium of Quantum Physics

With contributions by leading quantum physicists, philosophers and historians, this comprehensive A-to-Z of quantum physics provides a lucid understanding of key concepts of quantum theory and experiment. It covers technical and interpretational aspects alike, and includes both traditional and new concepts, making it an indispensable resource for concise, up-to-date information about the many facets of quantum physics.
## Statistical Structure of Quantum Theory

New ideas on the mathematical foundations of quantum mechanics, related to the theory of quantum measurement, as well as the emergence of quantum optics, quantum electronics and optical communications have shown that the statistical structure of quantum mechanics deserves special investigation. In the meantime it has become a mature subject. In this book, the author, himself a leading researcher in this field, surveys the basic principles and results of the theory, concentrating on mathematically precise formulations. Special attention is given to the measurement dynamics. The presentation is pragmatic, concentrating on the ideas and their motivation. For detailed proofs, the readers, researchers and graduate students, are referred to the extensively documented literature.
## Probability and Stochastic Processes for Engineers

## Quantum Computation and Quantum Information

One of the most cited books in physics of all time, Quantum Computation and Quantum Information remains the best textbook in this exciting field of science. This 10th anniversary edition includes an introduction from the authors setting the work in context. This comprehensive textbook describes such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography and quantum error-correction. Quantum mechanics and computer science are introduced before moving on to describe what a quantum computer is, how it can be used to solve problems faster than 'classical' computers and its real-world implementation. It concludes with an in-depth treatment of quantum information. Containing a wealth of figures and exercises, this well-known textbook is ideal for courses on the subject, and will interest beginning graduate students and researchers in physics, computer science, mathematics, and electrical engineering.
## Introduction to Photon Communication

In recent years, progress in the generation of squeezed states of light, mainly characterized by a reduced noise property, has stimulated important work in relation to their potential use to improve the sensitivity of optical communication systems. These notes are devoted to the detection and information processing of optical signals at very low levels of power. A survey of recent developments from the quantum and classical points of view is presented. Ultimate limits of performance under the criteria of detection and information are established. Some of the results are detailed and may be utilized for the design of practical systems of communication using present technology. The book addresses physicists and engineers interested in present and future developments in optical communications.
## Quantum Computing and Communications

Quantum computers will revolutionize the way telecommunications networks function. Quantum computing holds the promise of solving problems that would be intractable with conventional computers by implementing principles from quantum physics in the development of computer hardware, software and communications equipment. Quantum-assisted computing will be the first step towards full quantum systems, and will cause immense disruption of our traditional networks. The world’s biggest manufacturers are investing large amounts of resources to develop crucial quantum-assisted circuits and devices. Quantum Computing and Communications: Gives an overview of basic quantum computing algorithms and their enhanced versions such as efficient database searching, counting and phase estimation. Introduces quantum-assisted solutions for telecom problems including multi-user detection in mobile systems, routing in IP based networks, and secure ciphering key distribution. Includes an accompanying website featuring exercises (with solution manual) and sample algorithms from the classical telecom world, corresponding quantum-based solutions, bridging the gap between pure theory and engineering practice. This book provides telecommunications engineers, as well as graduate students and researchers in the fields of computer science and telecommunications, with a wide overview of quantum computing & communications and a wealth of essential, practical information.
## Probability, Random Processes, and Estimation Theory for Engineers

Disk contains: BASIC and MATLAB demonstration programs.
## Classical and Quantum Information

A new discipline, Quantum Information Science, has emerged in the last two decades of the twentieth century at the intersection of Physics, Mathematics, and Computer Science. Quantum Information Processing is an application of Quantum Information Science which covers the transformation, storage, and transmission of quantum information; it represents a revolutionary approach to information processing. Classical and Quantum Information covers topics in quantum computing, quantum information theory, and quantum error correction, three important areas of quantum information processing. Quantum information theory and quantum error correction build on the scope, concepts, methodology, and techniques developed in the context of their close relatives, classical information theory and classical error correcting codes. Presents recent results in quantum computing, quantum information theory, and quantum error correcting codes Covers both classical and quantum information theory and error correcting codes The last chapter of the book covers physical implementation of quantum information processing devices Covers the mathematical formalism and the concepts in Quantum Mechanics critical for understanding the properties and the transformations of quantum information
## Quantum Optics and the Spectroscopy of Solids

Remarkable recent progress in quantum optics has given rise to extremely precise quantum measurements that are used in the research into the fundamentals of quantum physics, and in different branches of physics such as optical spectroscopy. This progress stimulates new technologies in the field of optical communications, optical computation and information systems. This state-of-the-art volume presents work from a Summer School on Advances in Quantum Optics and Spectroscopy of Solids, held in Ankara, Turkey, in 1995. The various contributions written by leading scientists in the field cover a wide range of subjects in this exciting area of physics, and report new and important results and ideas. Topics dealt with include the interaction of quantum light with trapped atoms and condensed matter; quantum tomography and phase analysis; and many applications of quantum optics from mesoscopic physics to correlation spectroscopy of non-classical states, which are of major importance in understanding the nature of collective excitations in solids. Audience: This book will be of interest to postgraduate students and researchers whose work involves quantum optics, solid state spectroscopy and its applications.
## Linear Estimation

This original work offers the most comprehensive and up-to-date treatment of the important subject of optimal linear estimation, which is encountered in many areas of engineering such as communications, control, and signal processing, and also in several other fields, e.g., econometrics and statistics. The book not only highlights the most significant contributions to this field during the 20th century, including the works of Wiener and Kalman, but it does so in an original and novel manner that paves the way for further developments. This book contains a large collection of problems that complement it and are an important part of piece, in addition to numerous sections that offer interesting historical accounts and insights. The book also includes several results that appear in print for the first time. FEATURES/BENEFITS Takes a geometric point of view. Emphasis on the numerically favored array forms of many algorithms. Emphasis on equivalence and duality concepts for the solution of several related problems in adaptive filtering, estimation, and control. These features are generally absent in most prior treatments, ostensibly on the grounds that they are too abstract and complicated. It is the authors' hope that these misconceptions will be dispelled by the presentation herein, and that the fundamental simplicity and power of these ideas will be more widely recognized and exploited. Among other things, these features already yielded new insights and new results for linear and nonlinear problems in areas such as adaptive filtering, quadratic control, and estimation, including the recent "Ha theories."
## 23rd Midwest Symposium on Circuits and Systems, August 4-5, 1980, the University of Toledo, Toledo, Ohio

## Statistical Theory of Signal Detection

Statistical Theory of Signal Detection, Second Edition provides an elementary introduction to the theory of statistical testing of hypotheses that is related to the detection of signals in radar and communications technology. This book presents a comprehensive survey of digital communication systems. Organized into 11 chapters, this edition begins with an overview of the theory of signal detection and the typical detection problem. This text then examines the goals of the detection system, which are defined through an analogy with the testing of statistical hypotheses. Other chapters consider the noise fluctuations in terms of probability distributions whereby the statistical information is used to design a receiver that attains the maximum rate of successful detections in a long series of trials. This book discusses as well the criteria of success and failure in statistical situations. The final chapter deals with the types of stochastic signals. This book is a valuable resource for mathematicians and engineers.
## International Symposium on Mathematical Theory of Networks and Systems

## Linear Systems and Signals

Linear Systems and Signals, Third Edition, has been refined and streamlined to deliver unparalleled coverage and clarity. It emphasizes a physical appreciation of concepts through heuristic reasoning and the use of metaphors, analogies, and creative explanations. The text uses mathematics not only to prove axiomatic theory, but also to enhance physical and intuitive understanding. Hundreds of fully worked examples provide a hands-on, practical grounding of concepts and theory. Its thorough content, practical approach, and structural adaptability make Linear Systems and Signals, Third Edition, the ideal text for undergraduates.

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Author: Helstrom

Publisher: Academic Press

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Category: Mathematics

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Author: Carl W. Helstrom

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ISBN: 9780123400505

Category: Estimation theory

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Publisher: Springer Science & Business Media

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