This book gives an overview for practitioners and students of quantum physics and information science. It provides ready access to essential information on quantum information processing and communication, such as definitions, protocols and algorithms. Quantum information science is rarely found in clear and concise form. This book brings together this information from its various sources. It allows researchers and students in a range of areas including physics, photonics, solid-state electronics, nuclear magnetic resonance and information technology, in their applied and theoretical branches, to have this vital material directly at hand.
Author(s): Gregg Jaeger
Edition: 1
Publisher: Springer
Year: 2006
Language: English
Pages: 304
Tags: Информатика и вычислительная техника;Информационные технологии;
Cover......Page 1
Quantum Information......Page 3
ISBN-13: 9780387357256......Page 4
Foreword......Page 8
Preface......Page 12
Acknowledgments......Page 14
Contents......Page 16
1
Qubits......Page 21
1.1 Quantum state purity......Page 25
1.2 The representation of qubits......Page 28
1.3 Stokes parameters......Page 31
1.4 Single-qubit gates......Page 34
1.5 The double-slit experiment......Page 38
1.6 The Mach–Zehnder interferometer......Page 43
1.7 Quantum coherence and information processing......Page 45
2
Measurements and quantum operations......Page 49
2.1 The von Neumann classification of processes......Page 52
2.2 The Pauli classification of measurements......Page 54
2.3 Expectation values and the von Neumann projection......Page 55
2.4 The L¨uders rule......Page 57
2.5 Reduced statistical operators......Page 58
2.6 General quantum operations......Page 59
2.7 Positive-operator-valued measures......Page 61
3
Quantum nonlocality and interferometry......Page 65
3.1 Hidden variables and state completeness......Page 66
3.2 Von Neumann’s “no-go” theorem......Page 68
3.3 The Einstein–Podolsky–Rosen argument......Page 69
3.4 Gleason’s theorem......Page 71
3.5 Bell inequalities......Page 72
3.6 Interferometric complementarity......Page 77
3.7 The Franson interferometer......Page 81
3.8 Two-qubit quantum gates......Page 83
4
Classical information and communication......Page 87
4.1 Communication channels......Page 88
4.2 Shannon entropy......Page 90
4.4 Coding......Page 94
4.5 Error correction......Page 97
4.6 Data compression......Page 98
4.7 Communication complexity......Page 99
5
Quantum information......Page 101
5.1 Quantum entropy......Page 102
5.2 Quantum relative and conditional entropies......Page 104
5.3 Quantum mutual information......Page 105
5.4 Fidelity and coherent information......Page 106
5.5 Quantum R´enyi and Tsallis entropies......Page 108
6
Quantum entanglement......Page 111
6.1 Basic definitions......Page 112
6.2 The Schmidt decomposition......Page 114
6.3 Special bases and decompositions......Page 115
6.4 Stokes parameters and entanglement......Page 118
6.5 Partial transpose and reduction criteria......Page 119
6.6 The “fundamental postulate”......Page 121
6.7 Entanglement monotones......Page 122
6.8 Distillation and bound entanglement......Page 124
6.9 Entanglement and majorization......Page 125
6.10 Concurrence......Page 126
6.11 Entanglement witnesses......Page 127
6.12 Entanglement as a resource......Page 128
6.13 The thermodynamic analogy......Page 129
6.14 Information and the foundations of physics......Page 132
6.15 The geometry of entanglement......Page 134
6.16 Creating entangled photons......Page 135
7
Entangled multipartite systems......Page 141
7.1 Stokes and correlation tensors......Page 144
7.2 N-tangle......Page 146
7.4 Lorentz-group isometries......Page 147
7.5 Entanglement classes......Page 149
7.6 Algebraic invariants of multipartite systems......Page 151
7.7 Three-qubit states and residual tangle......Page 153
7.8 Three-qubit quantum logic gates......Page 155
7.9 States of higher qubit number......Page 156
8
Quantum state and process estimation......Page 159
8.1 Quantum state tomography......Page 160
8.2 Quantum process tomography......Page 163
8.3 Direct estimation methods......Page 164
9
Quantum communication......Page 167
9.1 Quantum channels......Page 168
9.2 Quantum channel capacities......Page 169
9.3 Holevo’s theorem......Page 171
9.4 Discrimination of quantum states......Page 173
9.5 The no-cloning theorem......Page 176
9.6 Basic quantum channels......Page 177
9.7 The GHJW theorem......Page 179
9.8 Quantum dense coding......Page 180
9.9 Quantum teleportation......Page 182
9.10 Entanglement “swapping”......Page 184
9.11 Entanglement “purification”......Page 185
9.12 Quantum data compression......Page 187
9.13 Quantum communication complexity......Page 189
10
Quantum decoherence and its mitigation......Page 191
10.1 Quantum decoherence......Page 192
10.2 Decoherence and mixtures......Page 193
10.3 Decoherence-free subspaces......Page 194
10.4 Quantum coding, error detection, and correction......Page 195
10.5 The nine-qubit Shor code......Page 199
10.6 Stabilizer codes......Page 201
10.7 Concatenation of quantum codes......Page 203
11.1 Quantum broadcasting......Page 205
11.2 Quantum copying......Page 206
11.3 Quantum deleting......Page 209
11.4 Landauer’s principle......Page 210
12.1 Cryptography and cryptosystems......Page 211
12.2 QKD systems......Page 213
12.3 The BB84 (four-state) protocol......Page 215
12.4 The E91 (Ekert) protocol......Page 217
12.5 The B92 (two-state) protocol......Page 218
12.7 Eavesdropping......Page 219
12.8 Security proofs......Page 221
13
Classical and quantum computing......Page 223
13.1 Classical computing and computational complexity......Page 224
13.2 Deterministic Turing machines......Page 226
13.3 Probabilistic Turing machines......Page 227
13.4 Multi-tape Turing machines......Page 228
13.5 Quantum Turing machines......Page 229
13.6 Quantum computational complexity......Page 231
13.7 Fault-tolerant quantum computing......Page 234
13.8 Linear optical quantum computation......Page 235
14
Quantum algorithms......Page 239
14.1 The Deutsch–Jozsa algorithm......Page 240
14.2 The Grover search algorithm......Page 241
14.3 The Shor factoring algorithm......Page 244
14.4 The Simon algorithm......Page 249
A.1 Boolean algebra and Galois fields......Page 251
A.2 Random variables......Page 252
A.3 Vector Spaces and Hilbert space......Page 253
A.5 The Dirac notation......Page 257
A.6 Groups of transformations......Page 259
A.7 Probability, lattices, and posets......Page 260
A.8 Projectors, correlations, and the Kochen–Specker
theorem......Page 262
A.9 Traditional quantum logic......Page 263
B.1 The standard postulates......Page 265
B.2 The Heisenberg–Robertson uncertainty relation......Page 267
References......Page 269
Index......Page 291
