Introduction to Quantum Computation and Information ( World Scientific )

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This is a pedagogical introduction to the subjects of quantum information and computation. Topics include non-locality of quantum mechanics, quantum computation, quantum cryptography, quantum error correction, and fault-tolerant quantum computation, as well as some experimental aspects of quantum computation and quantum cryptography. Only knowledge of basic quantum mechanics is assumed. Whenever more advanced concepts and techniques are used, they are introduced carefully. This book is designed to be a self-contained overview and is based on a series of lectures held at Hewlett-Packard Laboratories, Basic Research Institute in the Mathematical Sciences (BRIMS), Bristol, from November 1996 to April 1997, but it also includes other contributions.

Author(s): Hoi-Kwong Lo, Sandu Popescu , Tim Spiller
Year: 2001

Language: English
Pages: 364

CONTENTS......Page 14
FOREWORD......Page 6
PREFACE......Page 10
1 Introduction......Page 16
2 Quantum mechanics......Page 18
3 Quantum cryptography......Page 30
4 Quantum computing......Page 33
THE JOY OF ENTANGLEMENT......Page 44
1 What is entanglement?......Page 45
2 Hidden variables?......Page 48
3 A thought experiment......Page 49
4 Nonlocality......Page 51
5 Manipulating entanglement......Page 52
6 Thermodynamics and entanglement......Page 56
7 Entangled density matrices......Page 58
1 Quantum Information - What is it?......Page 64
2 Quantum Dense Coding......Page 68
3 Quantum Teleportation......Page 71
4 Density Matrices......Page 75
5 Compression of Information......Page 79
6 Von Neumann Entropy......Page 82
7 Schumacher Compression of Quantum Information......Page 85
8 Conclusions......Page 88
2 Novel Properties of Quantum Information......Page 91
3 An Illustrative Example: Quantum Money h......Page 96
4 Cryptography......Page 98
5 Quantum Key Distribution (QKD)......Page 102
6 Is Quantum Key Distribution Really Secure?......Page 108
7 Practical Considerations......Page 113
8 Beyond Quantum Key Distribution?......Page 115
9 Quantum Cryptanalysis......Page 124
10 Thoughts For The Future......Page 126
11 What Quantum Cryptography Is Telling Us About Quantum Mechanics?......Page 127
1 Introduction......Page 135
2 Standard polarization coding set-up......Page 136
3 Standard phase coding set-up......Page 138
4 QC using Faraday mirrors......Page 140
5 The performance of a QC-setup: transmission length, data rate and quantum bit error rate......Page 144
6 QC with single photon sources......Page 149
7 Practical eavesdropping......Page 150
8 Open air QC......Page 152
1 Computation and Physics......Page 158
2 Complexity theory......Page 159
3 Fundamental definitions......Page 164
4 Simple algorithm: Deutsch’s problem......Page 169
5 Simon’s problem......Page 171
6 Shor's factorisation algorithm......Page 175
7 Grover’s searching algorithm......Page 181
8 Towards Quantum Networks......Page 187
9 Coupling with the environment: the decoherence problem......Page 189
1 Introduction......Page 199
2 Three bit code......Page 200
3 Binary fields and discrete vector spaces......Page 203
4 Classical error correction......Page 206
5 Basic principles of quantum error correction......Page 211
6 Code construction and syndrome extraction......Page 218
7 Further development......Page 224
1 The need for fault tolerance......Page 228
2 Quantum error correction: the 7-qubit code......Page 232
3 Fault-tolerant recovery......Page 240
4 Fault-tolerant quantum gates......Page 252
5 The accuracy threshold for quantum computation......Page 258
6 Error models......Page 264
7 Topological Quantum Computation......Page 268
1 Introduction......Page 285
2 The ion-trap quantum computer......Page 287
3 The cavity quantum electrodynamics quantum computer......Page 300
4 Experimentally feasible quantum error-correction......Page 309
5 Quantum networking......Page 315
6 Conclusions......Page 322
1 Introduction......Page 326
2 Physics of Nuclear Magnetic Resonance......Page 329
3 Computation with NMR......Page 335
4 Theory of Bulk Quantum Computation......Page 339
5 Experimental Results......Page 344
1 Introduction......Page 355
2 Comparison of Classical and Quantum Information Processing......Page 356
3 Open Problems......Page 362