One-Dimensional Topological States of Synthetic Quantum Matter

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Topological states of matter are an influential concept of modern condensed matter physics with profound impact on our understanding of quantum phases. This dissertation is based on a collection of papers and addresses several questions on properties and applications of topological states in one-dimensional synthetic quantum systems. For example: - What is the fate of Majorana modes in systems with particle number conservation? - Can topologically protected edge modes be utilized for reliable transfer of quantum information? - How can one-dimensional topological quantum memories be implemented and corrected efficiently?