ISBN: 3-540-66778-4
TITLE: The Physics of Quantum Information
AUTHOR: Bouwmeester, Dirk; Ekert, Artur; Zeilinger, Anton (Eds.)
TOC:

1. The Physics of Quantum Information: Basic Concepts 1
1.1 Quantum Superposition 1
1.2 Qubits 3
1.3 Single-Qubit Transformations 4
1.4 Entanglement 7
1.5 Entanglement and Quantum Indistinguishability 9
1.6 The Controlled NOT Gate 11
1.7 The EPR Argument and Bell's Inequality 12
1.8 Comments 14
2. Quantum Cryptography 15
2.1 What is Wrong with Classical Cryptography? 15
2.1.1 From SCYTALE to ENIGMA 15
2.1.2 Keys and Their Distribution 16
2.1.3 Public Keys and Quantum Cryptography 19
2.1.4 Authentication: How to Recognise Cinderella ? 21
2.2 Quantum Key Distribution 22
2.2.1 Preliminaria 22
2.2.2 Security in Non-orthogonal States: No-Cloning Theorem 22
2.2.3 Security in Entanglement 24
2.2.4 What About Noisy Quantum Channels? 25
2.2.5 Practicalities 26
2.3 Quantum Key Distribution with Single Particles 27
2.3.1 Polarised Photons 27
2.3.2 Phase Encoded Systems 31
2.4 Quantum Key Distribution with Entangled States 33
2.4.1 Transmission of the Raw Key 33
2.4.2 Security Criteria 34
2.5 Quantum Eavesdropping 36
2.5.1 Error Correction 36
2.5.2 Privacy Amplification 37
2.6 Experimental Realisations 43
2.6.1 Polarisation Encoding 43
2.6.2 Phase Encoding 44
2.6.3 Entanglement-Based Quantum Cryptography 46
2.7 Concluding Remarks 47
3. Quantum Dense Coding and Quantum Teleportation 49
3.1 Introduction 49
3.2 Quantum Dense Coding Protocol 50
3.3 Quantum Teleportation Protocol 51
3.4 Sources of Entangled Photons 53
3.4.1 Parametric Down-Conversion 53
3.4.2 Time Entanglement 54
3.4.3 Momentum Entanglement 57
3.4.4 Polarisation Entanglement 58
3.5 Bell-State Analyser 60
3.5.1 Photon Statistics at a Beamsplitter 60
3.6 Experimental Dense Coding with Qubits 62
3.7 Experimental Quantum Teleportation of Qubits 67
3.7.1 Experimental Results 69
3.7.2 Teleportation of Entanglement 72
3.7.3 Concluding Remarks and Prospects 72
3.8 A Two-Particle Scheme for Quantum Teleportation 74
3.9 Teleportation of Continuous Quantum Variables 77
3.9.1 Employing Position and Momentum Entanglement 77
3.9.2 Quantum Optical Implementation 79
3.10 Entanglement Swapping: Teleportation of Entanglement 84
3.11 Applications of Entanglement Swapping 88
3.11.1 Quantum Telephone Exchange 88
3.11.2 Speeding up the Distribution of Entanglement 89
3.11.3 Correction of Amplitude Errors Developed due to Propagation 90
3.11.4 Entangled States of Increasing Numbers of Particles 91
4. Concepts of Quantum Computation 93
4.1 Introduction to Quantum Computation 93
4.1.1 A New Way of Harnessing Nature 93
4.1.2 From Bits to Qubits 94
4.1.3 Quantum Algorithms 98
4.1.4 Building Quantum Computers 100
4.1.5 Deeper Implications 101
4.1.6 Concluding Remarks 103
4.2 Quantum Algorithms 104
4.2.1 Introduction 104
4.2.2 Quantum Parallel Computation 105
4.2.3 The Principle of Local Operations 107
4.2.4 Oracles and Deutsch's Algorithm 109
4.2.5 The Fourier Transform and Periodicities 114
4.2.6 Shor's Quantum Algorithm for Factorisation 119
4.2.7 Quantum Searching and NP 121
4.3 Quantum Gates and Quantum Computation with Trapped Ions 126
4.3.1 Introduction 126
4.3.2 Quantum Gates with Trapped Ions 126
4.3.3 N Cold Ions Interacting with Laser Light 128
4.3.4 Quantum Gates at Nonzero Temperature 130
5. Experiments Leading Towards Quantum Computation 133
5.1 Introduction 133
5.2 Cavity QED-Experiments: Atoms in Cavities and Trapped Ions 134
5.2.1 A Two-Level System Coupled to a Quantum Oscillator 134
5.2.2 Cavity QED with Atoms and Cavities 135
5.2.3 Resonant Coupling: Rabi Oscillations and Entangled Atoms 137
5.2.4 Dispersive Coupling: Schrdinger's Cat and Decoherence 143
5.2.5 Trapped-Ion Experiments 147
5.2.6 Choice of Ions and Doppler Cooling 148
5.2.7 Sideband Cooling 150
5.2.8 Electron Shelving and Detection of Vibrational Motion 153
5.2.9 Coherent States of Motion 154
5.2.10 Wigner Function of the One-Phonon State 157
5.2.11 Squeezed States and Schrdinger Cats with Ions 159
5.2.12 Quantum Logic with a Single Trapped 9Be+ Ion 160
5.2.13 Comparison and Perspectives 161
5.3 Linear Ion Traps for Quantum Computation 163
5.3.1 Introduction 163
5.3.2 Ion Confinement in a Linear Paul Trap 164
5.3.3 Laser Cooling and Quantum Motion 167
5.3.4 Ion Strings and Normal Modes 169
5.3.5 Ions as Quantum Register 171
5.3.6 Single-Qubit Preparation and Manipulation 172
5.3.7 Vibrational Mode as a Quantum Data Bus 173
5.3.8 Two-Bit Gates in an Ion-Trap Quantum Computer 174
5.3.9 Readout of the Qubits 175
5.3.10 Conclusion 175
5.4 Nuclear Magnetic Resonance Experiments 177
5.4.1 Introduction 177
5.4.2 The NMR Hamiltonian 177
5.4.3 Building an NMR Quantum Computer 179
5.4.4 Deutsch's Problem 181
5.4.5 Quantum Searching and Other Algorithms 184
5.4.6 Prospects for the Future 185
5.4.7 Entanglement and Mixed States 188
5.4.8 The Next Few Years 188
6. Quantum Networks and Multi-Particle Entanglement 191
6.1 Introduction 191
6.2 Quantum Networks I: Entangling Particles at Separate Locations 192
6.2.1 Interfacing Atoms and Photons 192
6.2.2 Model of Quantum State Transmission 193
6.2.3 Laser Pulses for Ideal Transmission 195
6.2.4 Imperfect Operations and Error Correction 197
6.3 Multi-Particle Entanglement 197
6.3.1 GreenbergerHorneZeilinger states 197
6.3.2 The Conflict with Local Realism 198
6.3.3 A Source for Three-Photon GHZ Entanglement 200
6.3.4 Experimental Proof of GHZ Entanglement 204
6.3.5 Experimental Test of Local Realism Versus Quantum Mechanics 206
6.4 Entanglement Quantification 210
6.4.1 Schmidt Decomposition and von Neumann Entropy 210
6.4.2 Purification Procedures 212
6.4.3 Conditions for Entanglement Measures 214
6.4.4 Two Measures of Distance Between Density Matrices 216
6.4.5 Numerics for Two Spin 1/2 Particles 217
6.4.6 Statistical Basis of Entanglement Measure 219
7. Decoherence and Quantum Error Correction 221
7.1 Introduction 221
7.2 Decoherence 222
7.2.1 Decoherence: Entanglement Between Qubits and Environment 222
7.2.2 Collective Interaction and Scaling 224
7.2.3 Subspace Decoupled From Environment 225
7.2.4 Other Find of Couplings 225
7.3 Limits to Quantum Computation Due to Decoherence 227
7.4 Error Correction and Fault-Tolerant Computation 232
7.4.1 Symmetrisation Procedures 232
7.4.2 Classical Error Correction 234
7.4.3 General Aspects of Quantum Error Correcting Codes 236
7.4.4 The Three Qubit Code 237
7.4.5 The Quantum Hamming Bound 238
7.4.6 The Seven Qubit Code 239
7.4.7 Fault-Tolerant Computation 241
7.5 General Theory of Quantum Error Correction and Fault Tolerance 242
7.5.1 Digitisation of Noise 242
7.5.2 Error Operators, Stabiliser, and Syndrome Extraction 243
7.5.3 Code Construction 246
7.5.4 The Physics of Noise 248
7.5.5 Fault-Tolerant Quantum Computation 250
7.6 Frequency Standards 252
8. Entanglement Purification 261
8.1 Introduction 261
8.2 Principles of Entanglement Purification 261
8.3 Local Filtering 269
8.4 Quantum Privacy Amplification 271
8.5 Generalisation of Purification to Multi-Particle Entanglement 275
8.6 Quantum Networks II: Communication over Noisy Channels 281
8.6.1 Introduction 281
8.6.2 Ideal Communication 282
8.6.3 Correction of Transfer Errors: The Photonic Channel 283
8.6.4 Purification with Finite Means 285
8.7 Quantum Repeaters 288
References 294
Index 311
END
