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Generalized Relative Entropies, Entanglement Monotones and One-Shot Information Theory

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We introduce two relative entropy quantities called the min- and max-relative 
entropies and discuss their properties and operational meanings.

These relative entropies act as parent quantities for tasks such as data compression, information
transmission and entanglement manipulation in one-shot information theory. Moreover, they lead us to define entanglement monotones which have interesting operational interpretations.