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hayashi m asymptotic theory quantum statistic inference 2005

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Textbook in PDF format 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. Preface First Appearance List of Contributors Introduction to Quantum Statistical Inference Introduction to Part I Strong Converse and Stein’s Lemma in Quantum Hypothesis Testing The Proper Formula for Relative Entropy and its Asymptotics in Quantum Probability Strong Converse Theorems in Quantum Information Theory Asymptotics of Quantum Relative Entropy from a Representation Theoretical Viewpoint Quantum Birthday Problems: Geometrical Aspects of Quantum Random Coding Quantum Cram´er-Rao Bound in Mixed States Model Introduction to Part II A New Approach to Cram´er-Rao Bounds for Quantum State Estimation On Fisher Information of Quantum Statistical Models On the Parameter Estimation Problem for Quantum Statistical Models A Generalization of the Simultaneous Diagonalization of Hermitian Matrices and its Relation to Quantum Estimation Theory A Linear Programming Approach to Attainable Cram´er-Rao Type Bounds Statistical Model with Measurement Degree of Freedom and Quantum Physics Asymptotic Quantum Theory for the Thermal States Family State Estimation for Large Ensembles Quantum Cram´er-Rao Bound in Pure States Model Introduction to Part III Quantum Fisher Metric and Estimation for Pure State Models Geometry of Quantum Estimation Theory An Estimation Theoretical Characterization of Coherent States A Geometrical Approach to Quantum Estimation Theory Group Symmetric Approach to Pure States Model Introduction to Part IV Asymptotic Estimation Theory for a Finite-Dimensional Pure State Model Optimal Universal Quantum Cloning and State Estimation Bounds for Generalized Uncertainty of Shift Parameter Optimal Extraction of Information from Finite Quantum Ensembles Large Deviation Theory in Quantum Estimation Introduction to Part V On the Relation between Kullback Divergence and Fisher Information: From Classical Systems to Quantum Systems Two Quantum Analogues of Fisher Information from a Large Deviation Viewpoint of Quantum Estimation Estimating the Spectrum of a Density Operator Further Topics on Quantum Statistical Inference Introduction to Part VI Optimal Quantum Clocks Quantum Channel Identification Problem Homodyning as Universal Detection On the Measurement of Qubits Index

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hayashi m asymptotic theory quantum statistic inference 2005

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