Advanced Quantum Communications

SANDOR IMRE is head of the Department of Telecommunications at Budapest University of Technology and Economics in Budapest, Hungary. He has published over 250 peer-reviewed papers from global journals and at international conferences including many of IEEE COMSOC-sponsored conferences.
 
LASZLO GYONGYOSI is a PhD student and faculty member at Budapest University of Technology and Economics in Budapest, Hungary.

The authors explain quantum communication theory from an engineering(application) viewpoint including the advanced quantum communication schemes and give an overview on the security of these systems. Each section of the book addresses an area of major research of quantum information theory and quantum communication networks. The authors present the fundamental theoretical results of quantum information theory, and simultaneously present the details of advanced quantum communication protocols with clear mathematical and information theoretical background. The book will describe the engineering principles and questions of advanced communication network, quantum-Internet networks and intelligent quantum-probabilistic network controlling elements. The future quantum communication systems will integrate free-space and fiber-based ccommunication systems; However, the communication between them is the challenge. This book will bridge the gap between quantum physics, quantum information theory and practical engineering.

PREFACE xvii
 
CHAPTER 1 INTRODUCTION 1
 
1.1 Emerging Quantum Infl uences 2
 
1.2 Quantum Information Theory 2
 
1.3 Different Capacities of Quantum Channels 3
 
1.4 Challenges Related to Quantum Channel Capacities 5
 
1.5 Secret and Private Quantum Communication 6
 
1.6 Quantum Communications Networks 8
 
1.7 Recent Developments and Future Directions 9
 
CHAPTER 2 INTRODUCTION TO QUANTUM INFORMATION THEORY 11
 
2.1 Introduction 12
 
2.2 Basic Definitions and Formulas 15
 
2.3 Geometrical Interpretation of the Density Matrices 25
 
2.4 Quantum Entanglement 31
 
2.5 Entropy of Quantum States 34
 
2.6 Measurement of the Amount of Entanglement 43
 
2.7 Encoding Classical Information to Quantum States 49
 
2.8 Quantum Noiseless Channel Coding 54
 
2.9 Brief Summary 57
 
2.10 Further Reading 57
 
CHAPTER 3 THE CLASSICAL CAPACITIES OF QUANTUM CHANNELS 65
 
3.1 Introduction 65
 
3.2 From Classical to Quantum Communication Channels 73
 
3.3 Transmission of Classical Information over Quantum Channels 77
 
3.4 The Holevo-Schumacher-Westmoreland Theorem 84
 
3.5 Classical Communication over Quantum Channels 89
 
3.6 Brief Summary of Classical Capacities 98
 
3.7 Multilevel Quantum Systems and Qudit Channels 98
 
3.8 The Zero-Error Capacity of a Quantum Channel 100
 
3.9 Further Reading 117
 
CHAPTER 4 THE QUANTUM CAPACITY OF QUANTUM CHANNELS 126
 
4.1 Introduction 126
 
4.2 Transmission of Quantum Information 128
 
4.3 Quantum Coherent Information 136
 
4.4 The Asymptotic Quantum Capacity 146
 
4.5 Relation between Classical and Quantum Capacities of Quantum Channels 149
 
4.6 Further Reading 151
 
CHAPTER 5 GEOMETRIC INTERPRETATION OF QUANTUM CHANNELS 156
 
5.1 Introduction 156
 
5.2 Geometric Interpretation of the Quantum Channels 157
 
5.3 Geometric Interpretation of the Quantum Informational Distance 162
 
5.4 Computation of Smallest Quantum Ball to Derive the HSW Capacity 182
 
5.5 Illustrative Example 190
 
5.6 Geometry of Basic Quantum Channel Models 191
 
5.7 Geometric Interpretation of HSW Capacities of Different Quantum Channel Models 197
 
5.8 Further Reading 213
 
CHAPTER 6 ADDITIVITY OF QUANTUM CHANNEL CAPACITIES 218
 
6.1 Introduction 218
 
6.2 Additivity of Classical Capacity 223
 
6.3 Additivity of Quantum Capacity 225
 
6.4 Additivity of Holevo Information 232
 
6.5 Geometric Interpretation of Additivity of HSW Capacity 245
 
6.6 Classical and Quantum Capacities of some Channels 260
 
6.7 The Classical Zero-Error Capacities of some Quantum Channels 264
 
6.8 Further Reading 265
 
CHAPTER 7 SUPERACTIVATION OF QUANTUM CHANNELS 269
 
7.1 Introduction 270
 
7.2 The Non-Additivity of Private Information 270
 
7.3 Channel Combination for Superadditivity of Private Information 274
 
7.4 Superactivation of Quantum Capacity of Zero-Capacity Quantum Channels 282
 
7.5 Behind Superactivation: The Information Theoretic Description 295
 
7.6 Geometrical Interpretation of Quantum Capacity 302
 
7.7 Example of Geometric Interpretation of Superactivation 305
 
7.8 Extension of Superactivation for More General Classes 310
 
7.9 Superactivation of Zero-Error Capacities 315
 
7.10 Further Reading 322
 
CHAPTER 8 QUANTUM SECURITY AND PRIVACY 325
 
8.1 Introduction 326
 
8.2 Quantum Key Distribution 330

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