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Asymptotic Theory Of Quantum Statistical Inference
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Book Synopsis Asymptotic Theory of Quantum Statistical Inference by : Masahito Hayashi
Download or read book Asymptotic Theory of Quantum Statistical Inference written by Masahito Hayashi and published by World Scientific. This book was released on 2005-02-21 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: ' 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 '
Book Synopsis Asymptotic Theory of Quantum Statistical Inference by : Dagmar Bruss (physicien).)
Download or read book Asymptotic Theory of Quantum Statistical Inference written by Dagmar Bruss (physicien).) and published by . This book was released on 2005 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Statistical Experiments and Decisions by : A N Shiryaev
Download or read book Statistical Experiments and Decisions written by A N Shiryaev and published by World Scientific. This book was released on 2000-07-04 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an exposition of some fundamental aspects of the asymptotic theory of statistical experiments. The most important of them is “how to construct asymptotically optimal decisions if we know the structure of optimal decisions for the limit experiment”. Contents:Statistical Experiments and Their ComparisonConvergence of Statistical Experiments(γ,Γ)-Models. Convergence to (γ,Γ)-ModelsLocal Convergence of Statistical Experiments and Global EstimationStatistical Inference for Autoregressive Models of the First Order Readership: Researchers in probability and statistics. Keywords:Comparison of Statistical Experiments;Mixed Local Asymptotic Normality;Convergence of Experiments;Likelihood Ratio Processes;Contiguity;Autoregressive Models;Minimax Bound;Local Asymptotic NormalityReviews: “It is an interesting, welcome addition to the literature, and it contains many new insights. I congratulate the authors for writing this comprehensive monograph on a difficult subject.” Mathematical Reviews “The book is a highlight in modern mathematical statistics which offers a lot of new concepts. It recalls the brilliant methodology of Le Cam's Theory and the first chapters may be used as introduction into this field.” Mathematics Abstracts
Book Synopsis Quantum Information Theory by : Masahito Hayashi
Download or read book Quantum Information Theory written by Masahito Hayashi and published by Springer. This book was released on 2016-11-03 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate textbook provides a unified view of quantum information theory. Clearly explaining the necessary mathematical basis, it merges key topics from both information-theoretic and quantum- mechanical viewpoints and provides lucid explanations of the basic results. Thanks to this unified approach, it makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction) and quantum encryption. Since the publication of the preceding book Quantum Information: An Introduction, there have been tremendous strides in the field of quantum information. In particular, the following topics – all of which are addressed here – made seen major advances: quantum state discrimination, quantum channel capacity, bipartite and multipartite entanglement, security analysis on quantum communication, reverse Shannon theorem and uncertainty relation. With regard to the analysis of quantum security, the present book employs an improved method for the evaluation of leaked information and identifies a remarkable relation between quantum security and quantum coherence. Taken together, these two improvements allow a better analysis of quantum state transmission. In addition, various types of the newly discovered uncertainty relation are explained. Presenting a wealth of new developments, the book introduces readers to the latest advances and challenges in quantum information. To aid in understanding, each chapter is accompanied by a set of exercises and solutions.
Book Synopsis Quantum Information by : Masahito Hayashi
Download or read book Quantum Information written by Masahito Hayashi and published by Springer Science & Business Media. This book was released on 2006-04-20 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level textbook provides a unified viewpoint of quantum information theory that merges key topics from both the information-theoretic and quantum- mechanical viewpoints. The text provides a unified viewpoint of quantum information theory and lucid explanations of those basic results, so that the reader fundamentally grasps advances and challenges. This unified approach makes accessible such advanced topics in quantum communication as quantum teleportation, superdense coding, quantum state transmission (quantum error-correction), and quantum encryption.
Book Synopsis Selected Papers on Probability and Statistics by :
Download or read book Selected Papers on Probability and Statistics written by and published by American Mathematical Soc.. This book was released on 2009 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains translations of papers that originally appeared in the Japanese journal Sugaku. The papers range over a variety of topics in probability theory, statistics, and applications. This volume is suitable for graduate students and research mathematicians interested in probability and statistics.
Book Synopsis From Statistical Physics to Statistical Inference and Back by : P. Grassberger
Download or read book From Statistical Physics to Statistical Inference and Back written by P. Grassberger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physicists, when modelling physical systems with a large number of degrees of freedom, and statisticians, when performing data analysis, have developed their own concepts and methods for making the `best' inference. But are these methods equivalent, or not? What is the state of the art in making inferences? The physicists want answers. More: neural computation demands a clearer understanding of how neural systems make inferences; the theory of chaotic nonlinear systems as applied to time series analysis could profit from the experience already booked by the statisticians; and finally, there is a long-standing conjecture that some of the puzzles of quantum mechanics are due to our incomplete understanding of how we make inferences. Matter enough to stimulate the writing of such a book as the present one. But other considerations also arise, such as the maximum entropy method and Bayesian inference, information theory and the minimum description length. Finally, it is pointed out that an understanding of human inference may require input from psychologists. This lively debate, which is of acute current interest, is well summarized in the present work.
Book Synopsis Quantum Stochastics and Information by :
Download or read book Quantum Stochastics and Information written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantum Stochastics and Information by : V. P. Belavkin
Download or read book Quantum Stochastics and Information written by V. P. Belavkin and published by World Scientific. This book was released on 2008 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum stochastic calculus has become an indispensable tool in modern quantum physics, its effectiveness being illustrated by recent developments in quantum control which place the calculus at the heart of the theory. Quantum statistics is rapidly taking shape as an intrinsically quantum counterpart to classical statistics, motivated by advances in quantum engineering and the need for better statistical inference tools for quantum systems. This volume contains a selection of regulear research articles and reviews by leading researchers in quantum control, quantum statistics, quantum probability and quantum information. The selection offers a unified view of recent trends in quantum stochastics, highlighting the common mathematical language of Hilbert space operators, and the deep connections between classical and quantum stochastic phenomena.
Book Synopsis Finite Sample Analysis in Quantum Estimation by : Takanori Sugiyama
Download or read book Finite Sample Analysis in Quantum Estimation written by Takanori Sugiyama and published by Springer Science & Business Media. This book was released on 2014-01-15 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Quantum Probability and Related Topics by : Rolando Rebolledo
Download or read book Quantum Probability and Related Topics written by Rolando Rebolledo and published by World Scientific. This book was released on 2011-01-19 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains current work at the frontiers of research in quantum probability, infinite dimensional stochastic analysis, quantum information and statistics. It presents a carefully chosen collection of articles by experts to highlight the latest developments in those fields. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians. Contents:Existence of the Fock Representation for Current Algebras of the Galilei Algebra (L Accardi et al.)Modular Structures and Landau Levels (F Bagarello)On Spectral Approach to Pascal White Noise Functionals (A Barhoumi et al.)Spectral Analysis for Twisted Waveguides (P Briet)On the Classification of Invarient State of Generic Quantum Markov Semigroups: The Gaussian Gauge Invariant Case (S Hachicha)On Difficulties Appearing in the Study of Stochastic Volterra Equations (A Karczewska)Entanglement Protection and Generation in a Two-Atom System (M Orszag)Hilbert Molecules — Square Roots of Positive Maps (M Skeide)Multiparameter Quantum Stochastic Processes (W J Spring)and other papers Readership: Researchers in mathematical physics, stochastic analysis and probability and statistics. Keywords:Quantum Probability;Quantum Markov Semigroups;Entanglement;Quantum Information;Quantum Statistics;Quantum Dilations;Quantum Measurements;Non-Markovian Open Systems
Book Synopsis Epistemic Processes by : Inge S. Helland
Download or read book Epistemic Processes written by Inge S. Helland and published by Springer Nature. This book was released on 2021-10-15 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses a link between statistical theory and quantum theory based on the concept of epistemic processes. The latter are processes, such as statistical investigations or quantum mechanical measurements, that can be used to obtain knowledge about something. Various topics in quantum theory are addressed, including the construction of a Hilbert space from reasonable assumptions and an interpretation of quantum states. Separate derivations of the Born formula and the one-dimensional Schrödinger equation are given. In concrete terms, a Hilbert space can be constructed under some technical assumptions associated with situations where there are two conceptual variables that can be seen as maximally accessible. Then to every accessible conceptual variable there corresponds an operator on this Hilbert space, and if the variables take a finite number of values, the eigenspaces/eigenvectors of these operators correspond to specific questions in nature together with sharp answers to these questions. This paves a new way to the foundations of quantum theory. The resulting interpretation of quantum mechanics is related to Hervé Zwirn's recent Convivial Solipsism, but it also has some relations to Quantum Bayesianism and to Rovelli's relational quantum mechanics. Niels Bohr's concept of complementarity plays an important role. Philosophical implications of this approach to quantum theory are discussed, including consequences for macroscopic settings. The book will benefit a broad readership, including physicists and statisticians interested in the foundations of their disciplines, philosophers of science and graduate students, and anyone with a reasonably good background in mathematics and an open mind.
Book Synopsis Library of Congress Subject Headings by : Library of Congress
Download or read book Library of Congress Subject Headings written by Library of Congress and published by . This book was released on 2009 with total page 1928 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Library of Congress Subject Headings by : Library of Congress. Cataloging Policy and Support Office
Download or read book Library of Congress Subject Headings written by Library of Congress. Cataloging Policy and Support Office and published by . This book was released on 2009 with total page 1924 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Fascination of Probability, Statistics and their Applications by : Mark Podolskij
Download or read book The Fascination of Probability, Statistics and their Applications written by Mark Podolskij and published by Springer. This book was released on 2015-12-26 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collecting together twenty-three self-contained articles, this volume presents the current research of a number of renowned scientists in both probability theory and statistics as well as their various applications in economics, finance, the physics of wind-blown sand, queueing systems, risk assessment, turbulence and other areas. The contributions are dedicated to and inspired by the research of Ole E. Barndorff-Nielsen who, since the early 1960s, has been and continues to be a very active and influential researcher working on a wide range of important problems. The topics covered include, but are not limited to, econometrics, exponential families, Lévy processes and infinitely divisible distributions, limit theory, mathematical finance, random matrices, risk assessment, statistical inference for stochastic processes, stochastic analysis and optimal control, time series, and turbulence. The book will be of interest to researchers and graduate students in probability, statistics and their applications.
Book Synopsis Library of Congress Subject Headings: P-Z by : Library of Congress. Subject Cataloging Division
Download or read book Library of Congress Subject Headings: P-Z written by Library of Congress. Subject Cataloging Division and published by . This book was released on 1989 with total page 1546 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Library of Congress Subject Headings by : Library of Congress. Office for Subject Cataloging Policy
Download or read book Library of Congress Subject Headings written by Library of Congress. Office for Subject Cataloging Policy and published by . This book was released on 1992 with total page 1360 pages. Available in PDF, EPUB and Kindle. Book excerpt:
