Entanglement and decoherence foundations and modern trends ; [International Summer School on Quantum Information, at the Max-Planck Institute for the Physics of Complex Systems, in Dresden, in September 2005

Entanglement and (de-)coherence arguably define the central issues of concern in present day quantum information theory. Entanglement being a consequence of the quantum mechanical superposition principle for composite systems, a better understanding of the environment-induced destruction of coherent superposition states is required to devise novel strategies for harvesting quantum interference phenomena. The present book collects a series of advanced lectures on the theoretical foundations of this active research field, from mathematical aspects underlying quantum topology to mesoscopic transport theory. All lectures start out from an elementary level and proceed along a steep learning curve. This makes the material particularly suitable for student seminars on the more fundamental theoretical aspects of quantum information, and equally useful as supplementary reading for advanced lectures on this topic. Annotation Entanglement and (de- )coherence arguably define the central issues of concern in present day quantum information theory. Entanglement being a consequence of the quantum mechanical superposition principle for composite systems, a better understanding of the environment-induced destruction of coherent superposition states is required to devise novel strategies for harvesting quantum interference phenomena. The present book collects a series of advanced lectures on the theoretical foundations of this active research field, from mathematical aspects underlying quantum topology to mesoscopic transport theory. All lectures start out from an elementary level and proceed along a steep learning curve. This makes the material particularly suitable for student seminars on the more fundamental theoretical aspects of quantum information, and equally useful as supplementary reading for advanced lectures on this topic "The book collects a series of advanced lectures on the theoretical foundations of this active research field, from mathematical aspects underlying quantum topology to mesoscopic transport theory." "All lectures start out from an elementary level and proceed along a steel learning curve. This makes the material particularly suitable for student seminars on the more fundamental theoretical aspects of quantum information, and equally useful as supplementary reading for advanced lectures on this topic."--Jacket Geometry Of State Spaces / A. Uhlmann, B. Crell -- Basic Concepts Of Entangled States / F. Mintert, C. Viviescas, A. Buchleitner -- Topology And Quantum Computing / L.h. Kauffman, S.j. Lomonaco Jr. -- Enganglement In Phase Space / A.m. Ozorio De Almeida -- Introduction To Decoherence Theory / K. Hornberger -- Diffusive Spin Transport / C.a. Müller. A. Buchleitner, C. Viviescas, M. Tiersch (eds.). Includes Bibliographical References And Index. Front Matter....Pages I-X Geometry of State Spaces....Pages 1-60 Basic Concepts of Entangled States....Pages 61-86 Topology and Quantum Computing....Pages 87-156 Entanglement in Phase Space....Pages 157-219 Introduction to Decoherence Theory....Pages 221-276 Diffusive Spin Transport....Pages 277-314 Back Matter....Pages 315-320 Entanglement and (de-)coherence arguably define the central issues of concern in present day quantum information theory. This book describes mathematical aspects that underlie quantum topology and mesoscopic transport theory.