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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