Relative entropies and their use in quantum information theory

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This dissertation investigates relative entropies, also called generalized divergences, and how they can be used to characterize information-theoretic tasks in quantum information theory.

• The main goal is to further refine characterizations of the optimal rates for quantum source coding, state redistribution, and measurement compression with quantum side information via second order asymptotic expansions and strong converse theorems.
• The dissertation consists of a mathematical and an information-theoretic part.
• In the mathematical part, we focus on the $\alpha$-sandwiched R\'enyi divergence ($\alpha$-SRD).