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.

• PREFACE xvii CHAPTER 1 INTRODUCTION 11.1 Emerging Quantum Infl uences 21.2 Quantum Information Theory 21.3 Different Capacities of Quantum Channels 31.4 Challenges Related to Quantum Channel Capacities 51.5 Secret and Private Quantum Communication 61.6 Quantum Communications Networks 81.7 Recent Developments and Future Directions 9CHAPTER 2 INTRODUCTION TO QUANTUM INFORMATION THEORY 112.1 Introduction 122.2 Basic Definitions and Formulas 152.3 Geometrical Interpretation of the Density Matrices 252.4 Quantum Entanglement 312.5 Entropy of Quantum States 342.6 Measurement of the Amount of Entanglement 432.7 Encoding Classical Information to Quantum States 492.8 Quantum Noiseless Channel Coding 542.9 Brief Summary 572.10 Further Reading 57CHAPTER 3 THE CLASSICAL CAPACITIES OF QUANTUM CHANNELS 653.1 Introduction 653.2 From Classical to Quantum Communication Channels 733.3 Transmission of Classical Information over Quantum Channels 773.4 The Holevo-Schumacher-Westmoreland Theorem 843.5 Classical Communication over Quantum Channels 893.6 Brief Summary of Classical Capacities 983.7 Multilevel Quantum Systems and Qudit Channels 983.8 The Zero-Error Capacity of a Quantum Channel 1003.9 Further Reading 117CHAPTER 4 THE QUANTUM CAPACITY OF QUANTUM CHANNELS 1264.1 Introduction 1264.2 Transmission of Quantum Information 1284.3 Quantum Coherent Information 1364.4 The Asymptotic Quantum Capacity 1464.5 Relation between Classical and Quantum Capacities of Quantum Channels 1494.6 Further Reading 151CHAPTER 5 GEOMETRIC INTERPRETATION OF QUANTUM CHANNELS 1565.1 Introduction 1565.2 Geometric Interpretation of the Quantum Channels 1575.3 Geometric Interpretation of the Quantum Informational Distance 1625.4 Computation of Smallest Quantum Ball to Derive the HSW Capacity 1825.5 Illustrative Example 1905.6 Geometry of Basic Quantum Channel Models 1915.7 Geometric Interpretation of HSW Capacities of Different Quantum Channel Models 1975.8 Further Reading 213CHAPTER 6 ADDITIVITY OF QUANTUM CHANNEL CAPACITIES 2186.1 Introduction 2186.2 Additivity of Classical Capacity 2236.3 Additivity of Quantum Capacity 2256.4 Additivity of Holevo Information 2326.5 Geometric Interpretation of Additivity of HSW Capacity 2456.6 Classical and Quantum Capacities of some Channels 2606.7 The Classical Zero-Error Capacities of some Quantum Channels 2646.8 Further Reading 265CHAPTER 7 SUPERACTIVATION OF QUANTUM CHANNELS 2697.1 Introduction 2707.2 The Non-Additivity of Private Information 2707.3 Channel Combination for Superadditivity of Private Information 2747.4 Superactivation of Quantum Capacity of Zero-Capacity Quantum Channels 2827.5 Behind Superactivation: The Information Theoretic Description 2957.6 Geometrical Interpretation of Quantum Capacity 3027.7 Example of Geometric Interpretation of Superactivation 3057.8 Extension of Superactivation for More General Classes 3107.9 Superactivation of Zero-Error Capacities 3157.10 Further Reading 322CHAPTER 8 QUANTUM SECURITY AND PRIVACY 3258.1 Introduction 3268.2 Quantum Key Distribution 3308.3 Private Communication over the Quantum Channel 3338.4 Quantum Cryptographic Primitives 3368.5 Further Reading 354CHAPTER 9 QUANTUM COMMUNICATION NETWORKS 3629.1 Long-Distance Quantum Communications 3629.2 Levels of Entanglement Swapping 3689.3 Scheduling Techniques of Purifi cation 3719.4 Hybrid Quantum Repeater 3759.5 Probabilistic Quantum Networks 3829.6 Conclusions 3849.7 Further Reading 384CHAPTER 10 RECENT DEVELOPMENTS AND FUTURE DIRECTIONS 38810.1 Introduction 38810.2 Qubit Implementations 39110.3 Quantum CPUs 39610.4 Quantum Memories 40010.5 Further Reading 411NOTATIONS AND ABBREVIATIONS 413REFERENCES 420INDEX 455

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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.

• PREFACE xvii CHAPTER 1 INTRODUCTION 11.1 Emerging Quantum Infl uences 21.2 Quantum Information Theory 21.3 Different Capacities of Quantum Channels 31.4 Challenges Related to Quantum Channel Capacities 51.5 Secret and Private Quantum Communication 61.6 Quantum Communications Networks 81.7 Recent Developments and Future Directions 9CHAPTER 2 INTRODUCTION TO QUANTUM INFORMATION THEORY 112.1 Introduction 122.2 Basic Definitions and Formulas 152.3 Geometrical Interpretation of the Density Matrices 252.4 Quantum Entanglement 312.5 Entropy of Quantum States 342.6 Measurement of the Amount of Entanglement 432.7 Encoding Classical Information to Quantum States 492.8 Quantum Noiseless Channel Coding 542.9 Brief Summary 572.10 Further Reading 57CHAPTER 3 THE CLASSICAL CAPACITIES OF QUANTUM CHANNELS 653.1 Introduction 653.2 From Classical to Quantum Communication Channels 733.3 Transmission of Classical Information over Quantum Channels 773.4 The Holevo-Schumacher-Westmoreland Theorem 843.5 Classical Communication over Quantum Channels 893.6 Brief Summary of Classical Capacities 983.7 Multilevel Quantum Systems and Qudit Channels 983.8 The Zero-Error Capacity of a Quantum Channel 1003.9 Further Reading 117CHAPTER 4 THE QUANTUM CAPACITY OF QUANTUM CHANNELS 1264.1 Introduction 1264.2 Transmission of Quantum Information 1284.3 Quantum Coherent Information 1364.4 The Asymptotic Quantum Capacity 1464.5 Relation between Classical and Quantum Capacities of Quantum Channels 1494.6 Further Reading 151CHAPTER 5 GEOMETRIC INTERPRETATION OF QUANTUM CHANNELS 1565.1 Introduction 1565.2 Geometric Interpretation of the Quantum Channels 1575.3 Geometric Interpretation of the Quantum Informational Distance 1625.4 Computation of Smallest Quantum Ball to Derive the HSW Capacity 1825.5 Illustrative Example 1905.6 Geometry of Basic Quantum Channel Models 1915.7 Geometric Interpretation of HSW Capacities of Different Quantum Channel Models 1975.8 Further Reading 213CHAPTER 6 ADDITIVITY OF QUANTUM CHANNEL CAPACITIES 2186.1 Introduction 2186.2 Additivity of Classical Capacity 2236.3 Additivity of Quantum Capacity 2256.4 Additivity of Holevo Information 2326.5 Geometric Interpretation of Additivity of HSW Capacity 2456.6 Classical and Quantum Capacities of some Channels 2606.7 The Classical Zero-Error Capacities of some Quantum Channels 2646.8 Further Reading 265CHAPTER 7 SUPERACTIVATION OF QUANTUM CHANNELS 2697.1 Introduction 2707.2 The Non-Additivity of Private Information 2707.3 Channel Combination for Superadditivity of Private Information 2747.4 Superactivation of Quantum Capacity of Zero-Capacity Quantum Channels 2827.5 Behind Superactivation: The Information Theoretic Description 2957.6 Geometrical Interpretation of Quantum Capacity 3027.7 Example of Geometric Interpretation of Superactivation 3057.8 Extension of Superactivation for More General Classes 3107.9 Superactivation of Zero-Error Capacities 3157.10 Further Reading 322CHAPTER 8 QUANTUM SECURITY AND PRIVACY 3258.1 Introduction 3268.2 Quantum Key Distribution 3308.3 Private Communication over the Quantum Channel 3338.4 Quantum Cryptographic Primitives 3368.5 Further Reading 354CHAPTER 9 QUANTUM COMMUNICATION NETWORKS 3629.1 Long-Distance Quantum Communications 3629.2 Levels of Entanglement Swapping 3689.3 Scheduling Techniques of Purifi cation 3719.4 Hybrid Quantum Repeater 3759.5 Probabilistic Quantum Networks 3829.6 Conclusions 3849.7 Further Reading 384CHAPTER 10 RECENT DEVELOPMENTS AND FUTURE DIRECTIONS 38810.1 Introduction 38810.2 Qubit Implementations 39110.3 Quantum CPUs 39610.4 Quantum Memories 40010.5 Further Reading 411NOTATIONS AND ABBREVIATIONS 413REFERENCES 420INDEX 455

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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.

• PREFACE xvii CHAPTER 1 INTRODUCTION 11.1 Emerging Quantum Infl uences 21.2 Quantum Information Theory 21.3 Different Capacities of Quantum Channels 31.4 Challenges Related to Quantum Channel Capacities 51.5 Secret and Private Quantum Communication 61.6 Quantum Communications Networks 81.7 Recent Developments and Future Directions 9CHAPTER 2 INTRODUCTION TO QUANTUM INFORMATION THEORY 112.1 Introduction 122.2 Basic Definitions and Formulas 152.3 Geometrical Interpretation of the Density Matrices 252.4 Quantum Entanglement 312.5 Entropy of Quantum States 342.6 Measurement of the Amount of Entanglement 432.7 Encoding Classical Information to Quantum States 492.8 Quantum Noiseless Channel Coding 542.9 Brief Summary 572.10 Further Reading 57CHAPTER 3 THE CLASSICAL CAPACITIES OF QUANTUM CHANNELS 653.1 Introduction 653.2 From Classical to Quantum Communication Channels 733.3 Transmission of Classical Information over Quantum Channels 773.4 The Holevo-Schumacher-Westmoreland Theorem 843.5 Classical Communication over Quantum Channels 893.6 Brief Summary of Classical Capacities 983.7 Multilevel Quantum Systems and Qudit Channels 983.8 The Zero-Error Capacity of a Quantum Channel 1003.9 Further Reading 117CHAPTER 4 THE QUANTUM CAPACITY OF QUANTUM CHANNELS 1264.1 Introduction 1264.2 Transmission of Quantum Information 1284.3 Quantum Coherent Information 1364.4 The Asymptotic Quantum Capacity 1464.5 Relation between Classical and Quantum Capacities of Quantum Channels 1494.6 Further Reading 151CHAPTER 5 GEOMETRIC INTERPRETATION OF QUANTUM CHANNELS 1565.1 Introduction 1565.2 Geometric Interpretation of the Quantum Channels 1575.3 Geometric Interpretation of the Quantum Informational Distance 1625.4 Computation of Smallest Quantum Ball to Derive the HSW Capacity 1825.5 Illustrative Example 1905.6 Geometry of Basic Quantum Channel Models 1915.7 Geometric Interpretation of HSW Capacities of Different Quantum Channel Models 1975.8 Further Reading 213CHAPTER 6 ADDITIVITY OF QUANTUM CHANNEL CAPACITIES 2186.1 Introduction 2186.2 Additivity of Classical Capacity 2236.3 Additivity of Quantum Capacity 2256.4 Additivity of Holevo Information 2326.5 Geometric Interpretation of Additivity of HSW Capacity 2456.6 Classical and Quantum Capacities of some Channels 2606.7 The Classical Zero-Error Capacities of some Quantum Channels 2646.8 Further Reading 265CHAPTER 7 SUPERACTIVATION OF QUANTUM CHANNELS 2697.1 Introduction 2707.2 The Non-Additivity of Private Information 2707.3 Channel Combination for Superadditivity of Private Information 2747.4 Superactivation of Quantum Capacity of Zero-Capacity Quantum Channels 2827.5 Behind Superactivation: The Information Theoretic Description 2957.6 Geometrical Interpretation of Quantum Capacity 3027.7 Example of Geometric Interpretation of Superactivation 3057.8 Extension of Superactivation for More General Classes 3107.9 Superactivation of Zero-Error Capacities 3157.10 Further Reading 322CHAPTER 8 QUANTUM SECURITY AND PRIVACY 3258.1 Introduction 3268.2 Quantum Key Distribution 3308.3 Private Communication over the Quantum Channel 3338.4 Quantum Cryptographic Primitives 3368.5 Further Reading 354CHAPTER 9 QUANTUM COMMUNICATION NETWORKS 3629.1 Long-Distance Quantum Communications 3629.2 Levels of Entanglement Swapping 3689.3 Scheduling Techniques of Purifi cation 3719.4 Hybrid Quantum Repeater 3759.5 Probabilistic Quantum Networks 3829.6 Conclusions 3849.7 Further Reading 384CHAPTER 10 RECENT DEVELOPMENTS AND FUTURE DIRECTIONS 38810.1 Introduction 38810.2 Qubit Implementations 39110.3 Quantum CPUs 39610.4 Quantum Memories 40010.5 Further Reading 411NOTATIONS AND ABBREVIATIONS 413REFERENCES 420INDEX 455

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