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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.

Quantum theory --- Estimation theory --- Théorie quantique. --- Estimation, Théorie de l'.

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Mathematical statistics --- Estimation [Theorie de l' ] --- Estimation theory --- Schattingstheorie --- Théorie de l'estimation --- Estimating techniques --- Least squares --- Stochastic processes --- Estimation theory. --- Théorie de l'estimation

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Mathematical statistics --- Probabilities --- Estimation theory --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Risk --- Statistics, Mathematical --- Statistics --- Sampling (Statistics) --- Estimating techniques --- Stochastic processes --- Statistical methods --- Estimation theory. --- Probabilities. --- Mathematical statistics. --- Statistique mathématique --- Estimation, Théorie de l' --- Probabilités

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"Although numerical approximation and statistical inference are traditionally covered as entirely separate subjects, they are intimately connected through the common purpose of making estimations with partial information. This book explores these connections from a game and decision theoretic perspective, showing how they constitute a pathway to developing simple and general methods for solving fundamental problems in both areas. It illustrates these interplays by addressing problems related to numerical homogenization, operator adapted wavelets, fast solvers, and Gaussian processes. This perspective reveals much of their essential anatomy and greatly facilitates advances in these areas, thereby appearing to establish a general principle for guiding the process of scientific discovery. This book is designed for graduate students, researchers, and engineers in mathematics, applied mathematics, and computer science, and particularly researchers interested in drawing on and developing this interface between approximation, inference, and learning." [Publisher]

Approximation theory. --- Approximation, Théorie de l' --- Estimation theory. --- Estimation, Théorie de l' --- Mathematical statistics. --- Statistique mathématique. --- Approximation, Théorie de l' --- Estimation, Théorie de l' --- Statistique mathématique.

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Distribution (Probability theory) --- Estimation theory --- Nonparametric statistics --- AA / International- internationaal --- 303.6 --- Raming : theorie (wiskundige statistiek). Bayesian analysis and inference. --- Estimation theory. --- Nonparametric statistics. --- Distribution (Probability theory). --- Estimation, Théorie de l' --- Statistique non paramétrique --- Distribution-free statistics --- Statistics, Distribution-free --- Statistics, Nonparametric --- Estimating techniques --- Distribution functions --- Frequency distribution --- Raming : theorie (wiskundige statistiek). Bayesian analysis and inference --- Mathematical statistics --- Least squares --- Stochastic processes --- Characteristic functions --- Probabilities --- Estimation, Théorie de l'. --- Statistique non paramétrique.