Quantum Dynamics And Information - Proceedings Of The 46th Karpacz Winter School Of Theoretical Physics

Annotation The central theme of this lecture collection is quantum dynamics, regarded mostly as the dynamics of entanglement and that of decoherence phenomena. Both these concepts appear to refer to the behavior of surprisingly fragile features of quantum systems supposed to model quantum memories and to implement quantum date processing routines. This collection may serve as an essential resource for those interested in both theoretical description and practical applications of fundamentals of quantum mechanics 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 ......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 Quantum memories and Landauer's principle / R. Alicki -- Asymptotic entanglement in open quantum systems / F. Benatti -- Constructing positive maps in matrix algebras / D. Chruscinski and A. Kossakowski -- Quantum processes / M. Fannes and J. Wouters -- Pure state entanglement in terms of nilpotent variables : [symbol]-toolbox / A. Frydryszak -- Experiments on quantum coherence with cold atoms / W. Gawlik and A. Wojciechowski -- Dynamical entanglement of three-level atoms / L. Jakobczyk -- PPT states and measures of entanglement / W.A. Majewski -- Entanglement via nilpotent polynomials / A. Mandilara and V.M. Akulin -- Sudden death and sudden birth of entanglement / R. Tanas -- Open system dynamics of simple collision models / M. Ziman and V. Buzek PREFACE; CONTENTS; Quantum memories and Landauer's principle; Asymptotic entanglement in open quantum systems; Constructing positive maps in matrix algebras; Quantum processes; Pure state entanglement in terms of nilpotent variables:?-toolbox; Experiments on quantum coherence with cold atoms; Dynamical entanglement of three-level atoms; PPT states and measures of entanglement; Entanglement via nilpotent polynomials; Sudden death and sudden birth of entanglement; Open system dynamics of simple collision models; AUTHOR INDEX A lecture collection that deals with quantum dynamics, regarded mostly as the dynamics of entanglement and that of decoherence phenomena. It is suitable for those interested in both theoretical description and practical applications of fundamentals of quantum mechanics.