Quantum Information Processing with Finite Resources

Introduction.- Finite Resource Information Theory 1.2 Motivating Example.- Outline of the Book.- Modeling Quantum Information.- General Remarks on Notation.- Linear Operators and Events.- Functionals and States.- Multi-Partite Systems.- Functions on Positive Operators.- Quantum Channels.- Background and Further Reading.- Norms and Metrics.- Norms for Operators and Quantum States.- Trace Distance.- Fidelity.- Purified Distance.- Background and Further Reading.- Quantum Renyi Divergence.- Classical Renyi Divergence.- Classifying Quantum Renyi Divergences.- Minimal Quantum Renyi Divergence.- Petz Quantum Renyi Divergence.- Background and Further Reading.- Conditional Renyi Entropy.- Conditional Entropy from Divergence.- Definitions and Properties.-Duality Relations and their Applications.- Chain Rules.- Background and Further Reading.- Smooth Entropy Calculus.- Min- and Max-Entropy.- Smooth Entropies.- Properties of the Smooth Entropies.- Fully Quantum Asymptotic Equipartition Property.- Background and Further Reading.- Selected Applications.- Binary Quantum Hypothesis Testing.- Entropic Uncertainty Relations.- Randomness Extraction.- Background and Further Reading.- A Some Fundamental Matrix Analysis Results.- References.

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• Ciência dos materiais
• Teoria matemática da computação
• A física quântica (mecânica quântica e teoria quântica de campos)
• Algoritmos e estruturas de dados
• Teoria da informação
• Física da Matéria Condensada (física do estado sólido e estado líquido)

Entanglement;Information Processing;Quantum Channel;Quantum Computers;Quantum Cryptography;Quantum Device;Quantum Shannon Theory;Renyi Divergence;Renyi Entropy;Smooth Entropy