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Part Ⅰ Quantum optics and quantum information 3

1 The quantum theory of light 3

1.1 The classical electromagnetic field 3

1.2 Quantization of the electromagnetic field 6

1.3 Mode functions and polarization 16

1.4 Evolution of the field operators 25

1.5 Quantum states of the electromagnetic field 37

1.6 References and further reading 46

2 Quantum information processing 48

2.1 Quantum information 48

2.2 Quantum communication 57

2.3 Quantum computation with qubits 62

2.4 Quantum computation with continuous variables 80

2.5 References and further reading 89

3 Figures of merit 90

3.1 Density operators and superoperators 90

3.2 The fidelity 100

3.3 Entropy，information，and entanglement measures 101

3.4 Correlation functions and interference of light 105

3.5 Photon correlation measurements 108

3.6 References and further reading 110

Part Ⅱ Quantum information in photons and atoms 113

4 Photon sources and detectors 113

4.1 A mathematical model of photodetectors 113

4.2 Physical implementations of photodetectors 121

4.3 Single-photon sources 129

4.4 Entangled photon sources 139

4.5 Quantum non-demolition photon detectors 142

4.6 References and further reading 144

5 Quantum communication with single photons 145

5.1 Photons as information carriers 145

5.2 Quantum teleportation and entanglement swapping 162

5.3 Decoherence-free subspaces for communication 170

5.4 Quantum cryptography 172

5.5 References and further reading 177

6 Quantum computation with single photons 179

6.1 Optical N-port interferometers and scalability 179

6.2 Post-selection and feed-forward gates 181

6.3 Building quantum computers with probabilistic gates 192

6.4 Photon counting and quantum memories 202

6.5 Threshold theorem for linear-optical quantum computing 207

6.6 References and further reading 209

7 Atomic quantum information carriers 210

7.1 Atomic systems as qubits 210

7.2 The Jaynes-Cummings Hamiltonian 222

7.3 The optical master equation and quantum jumps 227

7.4 Entangling operations via path erasure 236

7.5 Other entangling gates 245

7.6 References and further reading 251

PartⅢ Quantum information in many-body systems 255

8 Quantum communication with continuous variables 255

8.1 Phase space in quantum optics 255

8.2 Continuous-variable entanglement 267

8.3 Teleportation and entanglement swapping 272

8.4 Entanglement distillation 280

8.5 Quantum cryptography 281

8.6 References and further reading 293

9 Quantum computation with continuous variables 294

9.1 Single-mode optical qunat gates 294

9.2 Two-mode Gaussian qunat operations 299

9.3 The Gottesman-Knill theorem for qunats 303

9.4 Nonlinear optical qunat gates 307

9.5 The one-way model for qunats 309

9.6 Quantum error correction for qunats 318

9.7 References and further reading 326

10 Atomic ensembles in quantum information processing 327

10.1 An ensemble of identical two-level atoms 327

10.2 Electromagnetically induced transparency 337

10.3 Quantum memories and quantum repeaters 344

10.4 The atomic ensemble as a single qubit 352

10.5 Photon-photon interactions via atomic ensembles 355

10.6 References and further reading 360

11 Solid-state quantum information carriers 361

11.1 Basic concepts of solid-state systems 361

11.2 Definition and optical manipulation of solid-state qubits 375

11.3 Interactions in solid-state qubit systems 381

11.4 Entangling two-qubit operations 384

11.5 Scalability of solid-state devices 393

11.6 References and further reading 395

12 Decoherence of solid-state qubits 397

12.1 Phonons 397

12.2 Electron phonon coupling 400

12.3 The master equation for electrons and phonons 403

12.4 Overcoming decoherence 406

12.5 Strong coupling effects 412

12.6 References and further reading 419

13 Quantum metrology 421

13.1 Parameter estimation and Fisher information 421

13.2 The statistical distance 425

13.3 The dynamical evolution of states 433

13.4 Entanglement-assisted parameter estimation 437

13.5 Optical quantum metrology 440

13.6 References and further reading 452

Appendix A Baker-Campbell-Haussdorff relations 454

Appendix B The Knill-Laflamme-Milburn protocol 457

Appendix C Cross-Kerr nonlinearities for single photons 462

References 465

Index 477