Quantum dynamics and information

CONTENTS......Page 10
PREFACE......Page 6
1. Introduction......Page 12
2. Stable classical memories......Page 14
3. Kitaev models......Page 15
4. Thermodynamics of information processing......Page 18
4.1. Landauer\'s Principle......Page 19
5. Two types of information?......Page 21
Bibliography......Page 22
1. Introduction......Page 24
2. Quantum systems in their environment......Page 25
3. Entanglement and dissipation......Page 27
3.1. Bipartite entanglement and its characterization......Page 28
3.2. Dissipative generation of entanglement......Page 31
4. Entropy and entanglement production......Page 34
5. Three open qubits in a symmetric environment......Page 37
5.1. Stationary states: general results......Page 38
5.2. Gaining entanglement by dissipation......Page 44
6. Conclusions......Page 45
Bibliography......Page 46
1. Introduction......Page 48
2. Preliminaries......Page 49
3. The structure of entanglement witnesses......Page 50
4.1. Choi map in M3(C)......Page 52
4.2. Robertson map in M4(C)......Page 54
5. Indecomposable maps in Md(C) — generalized Choi maps\n......Page 55
6. Positive maps from spectral conditions......Page 57
7. Bell-diagonal entanglement witnesses......Page 62
8. Indecomposable maps in M2k(C)......Page 64
Bibliography......Page 67
1. Introduction......Page 70
2. Classical Markov Processes......Page 72
3. Extending Quantum States......Page 74
4. Constructing Processes......Page 78
4.1. Hidden Markov Processes......Page 80
4.2. Qubits with SU(2)-invariance cont.......Page 81
4.3. Davies Maps......Page 83
4.4. Free Fermionic Processes......Page 84
5. Conclusion......Page 88
Bibliography......Page 89
1. Introduction......Page 90
2. Qubits and nilpotent commuting variables......Page 91
3. Canonical qubit relations......Page 93
4. Functions of nilpotent variables......Page 94
5. Generalized Hilbert space......Page 100
6. Factorization and entanglement chracterization in terms of η-functions determinants......Page 106
6.1. Factorization and entanglement measures of F( η1, η2)......Page 107
6.2. Factorization and entanglement measures of F(η1,η2, η3)......Page 108
6.3. Factorization and entanglement measures ofF( η1, η2, η3, η4)......Page 113
Acknowledgements......Page 122
Bibliography......Page 123
1. Introduction......Page 125
2.1. Two-level atom......Page 126
2.2. Two-level atom with angular momentum......Page 127
3. Manifestation of the coherence......Page 128
3.1. Light scattering......Page 129
3.2. Electromagnetically induced transparency......Page 130
3.3. Nonlinear Faraday Effect......Page 131
4. Nonlinear Faraday Effect with cold atoms......Page 133
4.1. High-field magnetometry......Page 135
6. Conclusions......Page 136
Bibliography......Page 137
1. Introduction......Page 139
2.2. Peres-Horodecki criterion and bound entanglement......Page 141
3. Time evolution of three-level atoms......Page 142
4. Generation of stationary distillable entanglement......Page 145
5. Delayed creation of distillable entanglement......Page 148
6. Conclusions......Page 151
Bibliography......Page 152
1. Introduction......Page 154
2. Positive maps......Page 155
3. PPT states......Page 158
4. Measures of entanglement......Page 161
Bibliography......Page 165
1. Some group-theory aspects of entanglement......Page 167
2. Canonic states of an assembly......Page 170
3. Extensive characteristics based on nilpotent polynomials: nilpotential and tanglemeter......Page 173
5. Examples: Canonic forms for two, three, and four qubits......Page 176
6. Quantum dynamics in terms of the nilpotent polynomials......Page 178
7. Entanglement beyond qubits......Page 181
8. Generalized entanglement......Page 184
9. A step toward mixed states of an assembly......Page 186
Bibliography......Page 189
1. Introduction......Page 190
2. Master equation......Page 192
3. Entanglement measure......Page 194
4. Entanglement evolution: zero temperature reservoir......Page 195
4.1. Creation of entanglement......Page 196
4.2. Sudden death of entanglement......Page 197
4.3. Sudden death and revival of entanglement......Page 199
4.4. Sudden birth of entanglement......Page 201
5. Entanglement evolution: thermal reservoir......Page 203
6. Conclusion......Page 207
Bibliography......Page 208
1. Open system dynamics......Page 210
1.1. Simple collision model......Page 211
1.2. Quantum channels......Page 212
2. Quantum homogenization as an analogue to thermalization......Page 213
2.1. Trivial homogenization......Page 215
2.2. Partial swap collisions......Page 216
2.3. System\'s convergence......Page 217
2.4. Stability of the reservoir......Page 218
2.5. Invariance of single-particle average state......Page 219
3. Quantum decoherence via collisions......Page 220
3.1. Simultaneous decoherence of the system and the environment......Page 221
4. Entanglement in collision models......Page 223
4.1. Entanglement in partial swap collision model......Page 225
4.2. Entanglement in controlled unitary collision model......Page 226
5.1. One-parametric semigroups......Page 228
5.2. Divisibility of channels......Page 229
5.3. Bloch sphere parametrization......Page 231
5.4. Master equation for homogenization collision model......Page 232
5.5. Master equation for decoherence collision model......Page 234
6. Conclusions......Page 236
Bibliography......Page 237
AUTHOR INDEX......Page 240