Notations xiii

Acknowledgements xv

Introduction xix

Chapter 1 Overview 1

1.1 Introduction 2

1.2 Quantum information 4

1.3 Quantum repeaters 10

1.4 Network architectures 15

1.5 Conclusions 20

Part 1 Fundamentals 23

Chapter 2 Quantum Background 25

2.1 Introduction 26

2.2 Schrodinger's equation 28

2.3 Qubits 29

2.4 Manipulating qubits 41

2.5 Bell pairs 47

2.6 The no-cloning theorem 53

2.7 Conclusion 54

Chapter 3 Networking Background 55

3.1 Concepts 56

3.2 Challenges in scaling up networks 63

3.3 Design patterns 65

3.4 The Internet 75

3.5 Conclusion 77

Chapter 4 Teleportation 79

4.1 The basic teleportation operation 79

4.2 Experimental demonstration of teleportation 82

4.3 State machines for teleportation 84

4.4 Teleporting gates 86

4.5 Conclusion 88

Part 2 Applications 91

Chapter 5 Quantum Key Distribution 93

5.1 QKD and the purpose of cryptography 94

5.2 BB84: single-photon QKD 97

5.3 E91: entanglement-based protocol 100

5.4 Using QKD 101

5.5 Existing QKD networks 105

5.6 Classical control protocols 109

5.7 Conclusion 111

Chapter 6 Distributed Digital Computation and Communication 113

6.1 Useful distributed quantum states 114

6.2 Coin flipping 118

6.3 Leader election 119

6.4 Quantum secret sharing 121

6.5 Byzantine agreement 126

6.6 Client-server and blind computation 128

6.7 Conclusion 130

Chapter 7 Entangled States as Reference Frames 131

7.1 Qubits in the environment 131

7.2 Distributed clock synchronization 135

7.3 Very long baseline optical interferometry 141

7.4 Conclusion 145

Part 3 Lines of Repeaters 147

Chapter 8 Physical Entanglement and Link-Layer Protocols 149

8.1 Creating entanglement using light 149

8.2 Memory and transceiver gubits 156

8.3 Link structure 161

8.4 State machines and protocol interactions 163

8.5 Managing density matrices in distributed software 164

8.6 Examples 169

8.7 Conclusion 173

Chapter 9 Purification 175

9.1 Measurement revisited 175

9.2 Basic purification 177

9.3 Scheduling purification 185

9.4 State machines and protocol interactions 187

9.5 More complex purification protocols 190

9.6 Experimental demonstrations 192

9.7 Conclusion 193

Chapter 10 Purfication and Entanglement Swapping-Based Repeaters 195

10.1 Hardware architectures 195

10.2 Getting from here to there 197

10.3 Nested purification session architecture 203

10.4 State machines and protocol interactions 206

10.5 Putting it all together 208

10.6 Considerations in the design of a simulator 215

10.7 Conclusion 217

Chapter 11 Quantum Error Correction-Based Repeaters 219

11.1 Quantum error correction 220

11.2 CSS repeaters 223

11.3 Surface code repeaters 230

11.4 Conclusion 235

Chapter 12 Finessing the Key Limitations 237

12.1 Quasi-asynchronous 238

12.2 Memoryless 244

12.3 Summary: comparing quantum communication approaches 247

12.4 Conclusion 251

Part 4 Networks of Repeaters 253

Chapter 13 Resource Management and Multiplexing 255

13.1 Simulated network and traffic 256

13.2 Simulations 259

13.3 Conclusion 263

Chapter 14 Routing 265

14.1 Introduction 265

14.2 Difficulties: differences between quantum and classical networks 267

14.3 Problems and solutions 268

14.4 Simulation and results 270

14.5 Conclusion 283

Chapter 15 Quantum Recursive Network Architecture 285

15.1 Review: network architecture 286

15.2 Recursive quantum requests 288

15.3 Implementing recursion in quantum networks 294

15.4 Example 295

15.5 Conclusion 298

Chapter 16 Coda 301

16.1 Future development 301

16.2 Open problems 303

16.3 Further readings for depth 304

16.4 Further readings for breadth 305

16.5 Final thoughts 307

Bibliograpy 309

Index 331