Titlebook: Quantum Information Processing with Finite Resources; Mathematical Foundat Marco Tomamichel Book 2016 The Author(s) 2016 Entanglement.Infor

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Selected Applications,, in particular the duality relation. Finally, smooth entropies were originally invented in the context of cryptography, and the Leftover Hashing Lemma reveals why this definition has proven so useful.

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Modeling Quantum Information,physical systems are ultimately governed by the laws of quantum mechanics. In this chapter we quickly review the relevant mathematical foundations of quantum theory and introduce notational conventions that will be used throughout the book.

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,Conditional Rényi Entropy,stem. The system as well as the side information can be either classical or a quantum. The goal in this chapter is to define conditional Rényi entropies that are operationally significant measures of this uncertainty, and to explore their properties. Unconditional entropies are then simply a special

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Smooth Entropy Calculus,lications it suffices to consider just two smooth Rényi entropies: the smooth min-entropy acts as a representative of all conditional Rényi entropies with ., whereas the smooth max-entropy acts as a representative for all Rényi entropies with .. These two entropies have particularly nice properties

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