"Broadly speaking, this book studies finite resource quantum information theory. ... A helpful table of notational conventions is given for easy reference. Norms and metrics for quantum states are discussed. ... each chapter ends with background and references for further reading. This book is at a suitable level for graduate students or researchers in physics or mathematics, with a reasonably strong linear algebra background." (Sarah Plosker, Mathematical Reviews, January, 2017)

• 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 Rényi Divergence.- Classical Rényi Divergence.- Classifying Quantum Rényi Divergences.- Minimal Quantum Rényi Divergence.- Petz Quantum Rényi Divergence.- Background and Further Reading.- Conditional Rényi 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.

"Broadly speaking, this book studies finite resource quantum information theory. ... A helpful table of notational conventions is given for easy reference. Norms and metrics for quantum states are discussed. ... each chapter ends with background and references for further reading. This book is at a suitable level for graduate students or researchers in physics or mathematics, with a reasonably strong linear algebra background." (Sarah Plosker, Mathematical Reviews, January, 2017)

• 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 Rényi Divergence.- Classical Rényi Divergence.- Classifying Quantum Rényi Divergences.- Minimal Quantum Rényi Divergence.- Petz Quantum Rényi Divergence.- Background and Further Reading.- Conditional Rényi 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.