This thesis offers novel strategies for the measurement of quantum correlations present in controllable quantum systems, as well as for a full-fledged implementation of the models of light-matter interaction through which these correlations can be generated. We propose the use of an ancillary qubit to efficiently access both time-correlation functions and entanglement monotones, and we provide two experimental demonstrations of our methods, measuring time correlations in an NMR setup and entanglement monotones in a photonic system. Moreover, we explain how time-correlation functions could be exploited for the quantum simulation of open quantum dynamics, and we provide an experimental recipe for the measurement of entanglement monotones in trapped ion technologies. On the other hand, we explore the quantum simulation of quantum optical models of light-matter interaction for inaccessible coupling regimes, providing experimental proposals for their implementation, both in ions and superconducting circuits. Finally, we also provide an experimental proposal for the quantum simulation of spin models in trapped ions following a digital-analog simulation scheme.
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