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This book provides an up-to-date account of current research in quantum information theory, at the intersection of theoretical computer science, quantum physics, and mathematics. The book confronts many unprecedented theoretical challenges generated by infinite dimensionality and memory effects in quantum communication. The book will also equip readers with all the required mathematical tools to understand these essential questions.
Preface
Introduction
Basic notation and preliminaries
Formulation of quantum systems
Probability measures and convex functions on S(ℍ)
Completely positive maps
Quantum channels and operations
Approximation and convergence of quantum channels
von Neumann entropy
Relative and conditional entropies
Channel output entropies
Quantum entanglement
Quantum mutual and coherent information
Holevo χ-capacity
Classical capacities of memoryless channels
Structure of quantum memory channels
Channels with Markovian memory
Channels with long-term memory
Bibliography
Index