edited by Masahito Hayashi
World Scientific Publishing 2005

Chapter 0 Introduction to Quantum Statistical Inference

Part I: Quantum Hypothesis Testing
Chapter 1 Introduction to Part I
Chapter 2 Strong Converse and Stein's Lemma in Quantum Hypothesis Testing
Tomohiro Ogawa and Hiroshi Nagaoka
Chapter 3 The Proper Formula for Relative Entropy and Its Asymptotics in Quantum Probability
Fumio Hiai and Denes Petz
Chapter 4 Strong Converse Theorems in Quantum Information Theory
Tomohiro Ogawa and Hiroshi Nagaoka
Chapter 5 Asymptotics of Quantum Relative Entropy from a Representation Theoretical Viewpoint
Masahito Hayashi
Chapter 6 Quantum Birthday Problems: Geometrical Aspects of Quantum Random Coding
Akio Fujiwara

Part II: Quantum Cramer-Rao Bound in Mixed States Model
Chapter 7 Introduction to Part II
Chapter 8 A New Approach to Cramer-Rao Bounds for Quantum State Estimation
Hiroshi Nagaoka
Chapter 9 On Fisher Information of Quantum Statistical Models
Hiroshi Nagaoka
Chapter 10 On the Parameter Estimation Problem for Quantum Statistical Models
Hiroshi Nagaoka
Chapter 11 A Generalization of the Simultaneous Diagonalization of Hermitian Matrices and its Relation to Quantum Estimation Theory
Hiroshi Nagaoka
Chapter 12 A Linear Programming Approach to Attainable Cramer-Rao Type Bounds
Masahito Hayashi
Chapter 13 Statistical Model with Measurement Degree of Freedom and Quantum Physics
Masahito Hayashi and Keiji Matsumoto
Chapter 14 Asymptotic Quantum Theory for the Thermal States Family
Masahito Hayashi
Chapter 15 State Estimation for Large Ensembles
Richard D. Gill and Serge Massar

Part III: Quantum Cramer-Rao Bound in Pure States Model
Chapter 16 Introduction to Part III
Chapter 17 Quantum Fisher Metric and Estimation for Pure State Models
Akio Fujiwara and Hiroshi Nagaoka
Chapter 18 Geometry of Quantum Estimation Theory
Akio Fujiwara
Chapter 19 An Estimation Theoretical Characterization of Coherent States
Akio Fujiwara and Hiroshi Nagaoka
Chapter 20 A Geometrical Approach of Quantum Estimation Theory
Keiji Matsumoto

Part IV: Group Symmetric Approach to Pure States Model
Chapter 21 Introduction to Part IV
Chapter 22 Optimal Extraction of Information from Finite Quantum Ensembles
Serge Massar and Sandu Popescu
Chapter 23 Asymptotic Estimation Theory for a Finite-dimensional Pure State Model
Masahito Hayashi
Chapter 24 Optimal Universal Quantum Cloning and State Estimation
Dagmar Bruss , Artur Ekert, and Chiara Macchiavello
Chapter 25 Bounds for Generalized Uncertainty of Shift Parameter
Alexander S. Holevo

Part V: Large Deviation Theory in Quantum Estimation
Chapter 26 Introduction to Part V
Chapter 27 On the Relation between Kullback Divergence and Fisher Information from Classical Systems to Quantum Systems
Hiroshi Nagaoka
Chapter 28 Two Quantum Analogues of Fisher Information from a Large Deviation Viewpoint of Quantum Estimation
Masahito Hayashi
Chapter 29 Estimating the Spectrum of a Density Operator
Michael Keyl and Reinhard F. Werner

Part VI: Further Topics on Quantum Statistical Inference
Chapter 30 Introduction to Part VI
Chapter 31 Optimal Quantum Clocks
Vladimir Buzek, R. Derka, and Serge Massar
Chapter 32 Quantum Channel Identification Problem
Akio Fujiwara
Chapter 33 Homodyning as Universal Detection
Giacomo Mauro D'Ariano
Chapter 34 Measurement of Qubits
Daniel F. V. James, Paul G. Kwiat, William J. Munro, and Andrew G. White