CONTENTS -- PREFACE -- Quantum memories and Landauer's principle -- 1. Introduction -- 2. Stable classical memories -- 3. Kitaev models -- 4. Thermodynamics of information processing -- 4.1. Landauer's Principle -- 4.2. Quantum memory as perpetuum mobile -- 5. Two types of information? -- Acknowledgments -- Bibliography -- Asymptotic entanglement in open quantum systems -- 1. Introduction -- 2. Quantum systems in their environment -- 2.1. 2 and 3 open qubits -- 3. Entanglement and dissipation -- 3.1. Bipartite entanglement and its characterization -- 3.2. Dissipative generation of entanglement -- 4. Entropy and entanglement production -- 5. Three open qubits in a symmetric environment -- 5.1. Stationary states: general results -- 5.2. Gaining entanglement by dissipation -- 6. Conclusions -- Bibliography -- Constructing positive maps in matrix algebras -- 1. Introduction -- 2. Preliminaries -- 3. The structure of entanglement witnesses -- 4. Basic indecomposable maps in low dimensions -- 4.1. Choi map in M3(C) -- 4.2. Robertson map in M4(C) -- 5. Indecomposable maps in Md(C) - generalized Choi maps -- 6. Positive maps from spectral conditions -- 7. Bell-diagonal entanglement witnesses -- 8. Indecomposable maps in M2k(C) -- 9. Conclusions -- Acknowledgments -- Bibliography -- Quantum processes -- 1. Introduction -- 2. Classical Markov Processes -- 3. Extending Quantum States -- 4. Constructing Processes -- 4.1. Hidden Markov Processes -- 4.2. Qubits with SU(2)-invariance cont. -- 4.3. Davies Maps -- 4.4. Free Fermionic Processes -- 5. Conclusion -- Acknowledgements -- Bibliography -- Pure state entanglement in terms of nilpotent variables: η-toolbox -- 1. Introduction -- 2. Qubits and nilpotent commuting variables -- 3. Canonical qubit relations -- 4. Functions of nilpotent variables -- 5. Generalized Hilbert space.

6. Factorization and entanglement chracterization in terms of η-functions determinants -- 6.1. Factorization and entanglement measures of F( η1, η2) -- 6.2. Factorization and entanglement measures of F(η1,η2, η3) -- 6.3. Factorization and entanglement measures ofF( η1, η2, η3, η4) -- 7. Conclusions -- Acknowledgements -- Bibliography -- Experiments on quantum coherence with cold atoms -- 1. Introduction -- 2. What is coherence? -- 2.1. Two-level atom -- 2.2. Two-level atom with angular momentum -- 3. Manifestation of the coherence -- 3.1. Light scattering -- 3.2. Electromagnetically induced transparency -- 3.3. Nonlinear Faraday Effect -- 4. Nonlinear Faraday Effect with cold atoms -- 4.1. High-field magnetometry -- 5. Quantum state engineering and quantum degeneracy -- 6. Conclusions -- Acknowledgments -- Bibliography -- Dynamical entanglement of three-level atoms -- 1. Introduction -- 2. Mixed-state entanglement and distillation -- 2.1. Distillability of entanglement -- 2.2. Peres-Horodecki criterion and bound entanglement -- 3. Time evolution of three-level atoms -- 4. Generation of stationary distillable entanglement -- 5. Delayed creation of distillable entanglement -- 6. Conclusions -- Bibliography -- PPT states and measures of entanglement -- 1. Introduction -- 2. Positive maps -- 3. PPT states -- 4. Measures of entanglement -- Acknowledgments -- Bibliography -- Entanglement via nilpotent polynomials -- 1. Some group-theory aspects of entanglement -- 2. Canonic states of an assembly -- 3. Extensive characteristics based on nilpotent polynomials: nilpotential and tanglemeter -- 4. Number of the parameters characterizing entanglement -- 5. Examples: Canonic forms for two, three, and four qubits -- 6. Quantum dynamics in terms of the nilpotent polynomials -- 7. Entanglement beyond qubits -- 8. Generalized entanglement.

9. A step toward mixed states of an assembly -- 10. Conclusion -- Bibliography -- Sudden death and sudden birth of entanglement -- 1. Introduction -- 2. Master equation -- 3. Entanglement measure -- 4. Entanglement evolution: zero temperature reservoir -- 4.1. Creation of entanglement -- 4.2. Sudden death of entanglement -- 4.3. Sudden death and revival of entanglement -- 4.4. Sudden birth of entanglement -- 5. Entanglement evolution: thermal reservoir -- 6. Conclusion -- Acknowledgements -- Bibliography -- Open system dynamics of simple collision models -- 1. Open system dynamics -- 1.1. Simple collision model -- 1.2. Quantum channels -- 2. Quantum homogenization as an analogue to thermalization -- 2.1. Trivial homogenization -- 2.2. Partial swap collisions -- 2.3. System's convergence -- 2.4. Stability of the reservoir -- 2.5. Invariance of single-particle average state -- 3. Quantum decoherence via collisions -- 3.1. Simultaneous decoherence of the system and the environment -- 4. Entanglement in collision models -- 4.1. Entanglement in partial swap collision model -- 4.2. Entanglement in controlled unitary collision model -- 5. Master equations for collision models -- 5.1. One-parametric semigroups -- 5.2. Divisibility of channels -- 5.3. Bloch sphere parametrization -- 5.4. Master equation for homogenization collision model -- 5.5. Master equation for decoherence collision model -- 6. Conclusions -- Acknowledgments -- Bibliography -- AUTHOR INDEX.