| A Guide for the Reader | p. 1 |
| Qubits, Cbits, Decoherence, Quantum Measurement and Environment | p. 3 |
| Lecturel-A Single Qubit: Basic Notions | p. 3 |
| Lecture 2 - Distinguishing Qubits from Cbits: Multi-qubit Systems and Quantum Computation | p. 10 |
| Lecture 3 - The Fundamental Theorem of Decoherence: "Isolated" Systems | p. 16 |
| Lecture 4 - Candidate Systems for Qubits: Preliminary Estimate of Decoherence Times | p. 22 |
| Lecture 5 - The Environment as a Bath of Oscillators: More Systematic Treatment of Decoherence | p. 30 |
| Lecture 6 - The Quantum Measurement Problem | p. 37 |
| Introduction to Quantum Computation | p. 47 |
| Physical Representation of Information | p. 47 |
| Qubits, Gates and Networks | p. 48 |
| Quantum Arithmetic and Function Evaluations | p. 53 |
| Algorithms and Their Complexity | p. 56 |
| From Interferometers to Computers | p. 59 |
| The First Quantum Algorithms | p. 63 |
| Quantum Search | p. 65 |
| Optimal Phase Estimation | p. 67 |
| Periodicity and Quantum Factoring | p. 69 |
| Cryptography | p. 71 |
| Environment-Induced Decoherence and the Transition from Quantum to Classical | p. 77 |
| Introduction and Overview | p. 77 |
| Quantum Measurements | p. 80 |
| Bit-by-Bit Measurement and Quantum Entanglement | p. 82 |
| Interactions and the Information Transfer in Quantum Measurements | p. 85 |
| Monitoring by the Environment and Decoherence | p. 87 |
| One-Bit Environment for a Bit-by-Bit Measurement | p. 88 |
| Decoherence of a Single (Qu)Bit | p. 90 |
| Decoherence, Einselection, and Controlled Shifts | p. 94 |
| Dynamics of Quantum Open Systems: Master Equations | p. 96 |
| Master Equation: Perturbative Evaluation | p. 97 |
| Example 1: Perturbative Master Equation in Quantum Brownian Motion | p. 100 |
| Example 2: Perturbative Master Equation for a Two-Level System Coupled to a Bosonic Heat Bath | p. 102 |
| Example 3: Perturbative Master Equation for a Particle Interacting with a Quantum Field | p. 105 |
| Exact Master Equation for Quantum Brownian Motion | p. 106 |
| Einselection in Quantum Brownian Motion | p. 112 |
| Decoherence of a Superposition of Two Coherent States | p. 112 |
| Predictability Sieve and Preferred States for QBM | p. 115 |
| Energy Eigenstates Can Also Be Selected by the Environment! | p. 117 |
| Deconstructing Decoherence: Landscape Beyond the Standard Models | p. 118 |
| Saturation of the Decoherence Rate at Large Distances | p. 119 |
| Decoherence at Zero Temperature | p. 120 |
| Preexisting Correlations Between the System and the Environment | p. 122 |
| Decoherence and Chaos | p. 125 |
| Quantum Predictability Horizon: How the Correspondence Is Lost | p. 125 |
| Exponential Instability vs. Decoherence | p. 127 |
| The Arrow of Time: A Price of Classicality? | p. 129 |
| Decoherence, Einselection, and the Entropy Production | p. 132 |
| How to Fight Against Decoherence: Quantum Error Correcting Codes | p. 133 |
| How to Protect a Classical Bit | p. 134 |
| How to Protect a Quantum Bit | p. 134 |
| Stabilizer Quantum Error-Correcting Codes | p. 140 |
| Discussion | p. 143 |
| Quantum Information Science Using Photons | p. 149 |
| Introduction | p. 149 |
| A Humble Point of View | p. 149 |
| Quantum Mystery | p. 150 |
| Maxwell's Demon | p. 151 |
| Shannon Entropy | p. 154 |
| Von Neumann Entropy | p. 156 |
| Einstein-Podolsky-Rosen Paradox and Bell's Inequalities | p. 157 |
| Producing Entangled Particles | p. 159 |
| Introduction | p. 159 |
| Parametric Down-Conversion | p. 159 |
| Franson's Proposal | p. 160 |
| Polarization Entanglement | p. 161 |
| The Beam Splitter Action on a Two-Photon State | p. 163 |
| Beamsplitter Transformation | p. 163 |
| Bell-State Analyzer | p. 164 |
| No-Cloning Theorem | p. 165 |
| Quantum Cryptography | p. 167 |
| Quantum Dense Coding | p. 169 |
| Theoretical Scheme | p. 169 |
| Experimental Dense Coding with Qubits | p. 170 |
| Quantum Teleportation | p. 171 |
| Theoretical Scheme | p. 171 |
| Experimental Quantum Teleportation of Qubits | p. 173 |
| Teleportation of Entanglement | p. 174 |
| A Two-Particle Scheme for Quantum Teleportation | p. 174 |
| Teleportation of Continuous Quantum Variables | p. 177 |
| Theoretical Scheme | p. 177 |
| Quantum Optical Implementation | p. 178 |
| Quantum Error Detection and Correction | p. 181 |
| Introduction | p. 181 |
| Quantum Error Detection | p. 181 |
| Avoiding Controlled-NOT Operations | p. 183 |
| Post-selection | p. 184 |
| Stimulated Entanglement | p. 185 |
| Theory | p. 185 |
| Bohm-Type Spin-s Entanglements | p. 193 |
| Quantum Information: Entanglement, Purification, Error Correction, and Quantum Optical Implementations | p. 199 |
| Introduction | p. 199 |
| Quantum Computers: Quantum Optical Implementations | p. 200 |
| Introduction | p. 200 |
| How to Construct a Quantum Computer | p. 201 |
| Physical Implementations for Quantum Computation | p. 202 |
| Quantum Optical Systems for Quantum Computation | p. 202 |
| Quantum Computation with Trapped Ions | p. 203 |
| Decoherence and Error Correction | p. 205 |
| Introduction | p. 205 |
| Decoherence | p. 205 |
| Error Correction | p. 206 |
| Error Correction and Decoherence | p. 209 |
| Entanglement of Pure States | p. 210 |
| Introduction | p. 210 |
| 2-Partite Entanglement: Definition | p. 211 |
| 2-Partite Entanglement: Qualifying and Quantifying | p. 212 |
| Multipartite Entanglement | p. 214 |
| Entanglement of Mixed States | p. 215 |
| Introduction | p. 215 |
| 2-Partite Entanglement: Definition | p. 217 |
| 2-Partite Entanglement: Entanglement Witnesses | p. 219 |
| 2-Partite Entanglement: Positive Maps | p. 220 |
| 2-Partite Entanglement: Entangled States with Positive Partial Transposition | p. 224 |
| Multipartite Entanglement | p. 224 |
| Entanglement Distillation | p. 226 |
| Introduction | p. 226 |
| Generalized Measurements | p. 227 |
| Distillation of Pure States | p. 229 |
| Distillation of Mixed States | p. 231 |
| Multipartite Distillation | p. 236 |
| Spintronics, Quantum Computing, and Quantum Communication in Quantum Dots | p. 241 |
| Introduction | p. 241 |
| Quantum Computing | p. 242 |
| Quantum Communication | p. 242 |
| General Remarks on Quantum Dots | p. 243 |
| Phase Coherence | p. 243 |
| Pulsed Switching and Adiabaticity | p. 245 |
| Initialization of a Quantum Register | p. 247 |
| Two-Qubit Operations in Coupled Quantum Dots | p. 247 |
| Laterally Coupled Dots | p. 248 |
| Vertically Coupled Dots | p. 250 |
| Singlet-Triplet Entangling Gate | p. 253 |
| Single-Spin Operations | p. 253 |
| Single-Spin Measurement | p. 254 |
| Spin Measurements Through Spontaneous Magnetization | p. 254 |
| Spin Measurements via the Charge | p. 254 |
| Quantum Dot as Spin Filter and Read-Out/Memory Device | p. 255 |
| Optical Measurements | p. 257 |
| Quantum Communication with Entangled Electrons | p. 257 |
| Adding Entangled Electrons to the Fermi Sea | p. 257 |
| Shot Noise of Entangled Electrons | p. 258 |
| Spin-Dependent Current Through a Double Dot-Probing Entanglement | p. 260 |
| Double Dot with Superconducting Leads | p. 262 |
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