0.1 Invitation to Quantum Information Theory

0.2 History of Quantum Information Theory

0.3 Structure of This Book

1.1 Quantum Systems and Linear Algebra

1.2 State and Measurement in Quantum Systems

1.3 Quantum Two-Level Systems

1.4 Composite Systems and Tensor Products

1.5 Matrix Inequalities and Matrix Monotone Functions

2.1 Information Quantities in Classical Systems

2.2 Extensions to Quantum Systems

2.3 Geometry of Probability Distribution Family

2.4 Estimation in Classical Systems

2.5 Type Method and Large Deviation Evaluation

2.6 Related Books

3.1 Two-State Discrimination in Quantum Systems

3.2 Discrimination of Plural Quantum States

3.3 Asymptotic Analysis of State Discrimination

3.4 Hypothesis Testing and Stein's Lemma

3.5 Hypothesis Testing by Separable Measurements

3.6 Proof of Direct Part of Stein's Lemma

3.7 Information Inequalities and Proof of Converse Part of Stein's Lemma

3.8 Historical Note

4.1 Formulation of Channel Coding Process in Quantum System

4.2 Coding Protocols with Adaptive Decoding and Feedback

4.3 Channel Capacities under Cost Constraint

4.4 A Fundamental Lemma

4.5 Proof of Direct Part of Classical-Quantum Channel Coding Theorem

4.6 Proof of Converse Part of Classical-Quantum Channel Coding Theorem

4.7 Pseudo Classical Channels

4.8 Historical Note

5.1 Description of State Evolution in Quantum Systems

5.2 Examples of Trace-Preserving Completely Positive Maps

5.3 State Evolutions in Quantum Two-Level Systems

5.4 Information-Processing Inequalities in Quantum Systems

5.5 Entropy Inequalities in Quantum Systems

5.6 Historical Note

6.1 Inner Products in Quantum Systems

6.2 Metrics induced Inner Products

6.3 Geodesics and Divergences

6.4 Quantum State Estimation

6.5 Large Deviation Evaluation

6.6 Multi-Parameter Estimation

6.7 Historical Note

7.1 State Reduction due to Quantum Measurement

7.2 Uncertainty and Measurement

7.3 Measurements with Negligible State Demolition

7.4 Historical Note

8.1 Entanglement and Local Quantum Operations

8.2 Fidelity and Entanglement

8.3 Entanglement and Information Quantities

8.4 Entanglement and Majorization

8.5 Distillation of Maximally Entangled States

8.6 Dilution of Maximally Entangled State

8.7 Unified Approach to Distillation and Dilution

8.8 Dilution with zero-rate communication

8.9 State Generation From Shared Randomness

8.10 Positive Partial Transpose (PPT) Operation

8.11 Examples

8.12 Historical Note

9.1 Quantum Teleportation

9.2 Classical-Quantum Channel Coding with Entangled Inputs

9.3 Classical-Quantum Channel Coding with Shared Entanglement

9.4 Quantum Channel Resolvability

9.5 Quantum Channel Communications with an Eavesdropper

9.6 The Channel Capacity for Quantum State Transmission

9.7 Examples

9.8 Historical Note

10.1 Four Kinds of Source Coding Schemes in Quantum Systems

10.2 Quantum Fixed-length Source Coding

10.3 Construction of a Quantum Fixed-length Source Code

10.4 Universal Quantum Fixed-length Source Codes

10.5 Universal Quantum Variable-length Source Codes

10.6 Mixed States Case

10.7 Compression by Classical Memory

10.8 Compression with Shared Randomness

10.9 Relation to Channel Capacities

10.10 Historical Note