Characterizing high-dimensional entanglement and coherence

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Entanglement and coherence are fundamental phenomena in quantum mechanics; moreover, they play a central role in quantum information processing. The characterization of these effects is often restricted to low-dimensional systems such as qubits, which simplifies the problem. In recent years, however, experimental progress enabled the control of high-dimensional quantum systems and theoretical works demonstrated potential advantages of information processing in the high-dimensional case. This project aims at a full understanding of entanglement and coherence in high-dimensional quantum systems. We consider different notions of high-dimensional and multi-level entanglement and coherence, and characterize them via analytical criteria and algorithmic approaches. Furthermore, we study their usefulness for tasks like quantum metrology or randomness generation. The project deepens the general understanding of quantum correlations and also provides useful tools for quantum optics experiments and implementations of quantum information processing.