Finite Sample Analysis in Quantum Estimation
Author | : Takanori Sugiyama |
Publisher | : |
Total Pages | : 132 |
Release | : 2014-02-28 |
Genre | : |
ISBN | : 9784431547785 |
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Author | : Takanori Sugiyama |
Publisher | : |
Total Pages | : 132 |
Release | : 2014-02-28 |
Genre | : |
ISBN | : 9784431547785 |
Author | : Takanori Sugiyama |
Publisher | : Springer Science & Business Media |
Total Pages | : 125 |
Release | : 2014-01-15 |
Genre | : Science |
ISBN | : 4431547770 |
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.
Author | : Luigi Accardi |
Publisher | : World Scientific |
Total Pages | : 469 |
Release | : 2008-03-10 |
Genre | : Science |
ISBN | : 9814471712 |
The purpose of this volume is examine bio-informatics and quantum information, which are growing rapidly at present, and to attempt to connect the two, with a view to enumerating and solving the many fundamental problems they entail. To this end, we look for interdisciplinary bridges in mathematics, physics, and information and life sciences. In particular, research into a new paradigm for information science and life science on the basis of quantum theory is emphasized.
Author | : Ryszard Horodecki |
Publisher | : IOS Press |
Total Pages | : 272 |
Release | : 2010 |
Genre | : Computers |
ISBN | : 1607505460 |
Theory and Implementation. This volume contains papers presented at the NATO Advanced Research Workshop September 9-12, 2009, Quantum Cryptography and Computing Theory and Implementation, that was held in Sopot, Poland and organized by the National Quantum Information Centre of
Author | : Nguyen Ngoc Thach |
Publisher | : Springer Nature |
Total Pages | : 865 |
Release | : 2022-05-28 |
Genre | : Technology & Engineering |
ISBN | : 3030986896 |
This book overviews latest ideas and developments in financial econometrics, with an emphasis on how to best use prior knowledge (e.g., Bayesian way) and how to best use successful data processing techniques from other application areas (e.g., from quantum physics). The book also covers applications to economy-related phenomena ranging from traditionally analyzed phenomena such as manufacturing, food industry, and taxes, to newer-to-analyze phenomena such as cryptocurrencies, influencer marketing, COVID-19 pandemic, financial fraud detection, corruption, and shadow economy. This book will inspire practitioners to learn how to apply state-of-the-art Bayesian, quantum, and related techniques to economic and financial problems and inspire researchers to further improve the existing techniques and come up with new techniques for studying economic and financial phenomena. The book will also be of interest to students interested in latest ideas and results.
Author | : |
Publisher | : |
Total Pages | : 574 |
Release | : 1970 |
Genre | : Weights and measures |
ISBN | : |
Author | : Masahito Hayashi |
Publisher | : World Scientific |
Total Pages | : 553 |
Release | : 2005-02-21 |
Genre | : Science |
ISBN | : 981448198X |
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.
Author | : Yong Siah Teo |
Publisher | : World Scientific |
Total Pages | : 396 |
Release | : 2015-08-20 |
Genre | : Science |
ISBN | : 9814678864 |
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.
Author | : Brian L. Joiner |
Publisher | : |
Total Pages | : 512 |
Release | : 1970 |
Genre | : Annals of mathematical statistics |
ISBN | : |
All articles, notes, queries, corrigenda, and obituaries appearing in the following journals during the indicated years are indexed: Annals of mathematical statistics, 1961-1969; Biometrics, 1965-1969#3; Biometrics, 1951-1969; Journal of the American Statistical Association, 1956-1969; Journal of the Royal Statistical Society, Series B, 1954-1969,#2; South African statistical journal, 1967-1969,#2; Technometrics, 1959-1969.--p.iv.
Author | : Nalini Anantharaman |
Publisher | : Springer Nature |
Total Pages | : 449 |
Release | : 2020-11-21 |
Genre | : Mathematics |
ISBN | : 3030564096 |
The volume presents extensive research devoted to a broad spectrum of mathematical analysis and probability theory. Subjects discussed in this Work are those treated in the so-called Strasbourg–Zürich Meetings. These meetings occur twice yearly in each of the cities, Strasbourg and Zürich, venues of vibrant mathematical communication and worldwide gatherings. The topical scope of the book includes the study of monochromatic random waves defined for general Riemannian manifolds, notions of entropy related to a compact manifold of negative curvature, interacting electrons in a random background, lp-cohomology (in degree one) of a graph and its connections with other topics, limit operators for circular ensembles, polyharmonic functions for finite graphs and Markov chains, the ETH-Approach to Quantum Mechanics, 2-dimensional quantum Yang–Mills theory, Gibbs measures of nonlinear Schrödinger equations, interfaces in spectral asymptotics and nodal sets. Contributions in this Work are composed by experts from the international community, who have presented the state-of-the-art research in the corresponding problems treated. This volume is expected to be a valuable resource to both graduate students and research mathematicians working in analysis, probability as well as their interconnections and applications.