Questions about the topological structure of our Universe are unanswered by the theory of relativity and are expected to be explained by a full theory of quantum gravity. In this talk, we will analyze how the topology of our Universe influences both vacuum fluctuations and vacuum entanglement. We will see in what ways and to what extent particle detectors are sensitive to the underlying topology of the Universe, and we will discuss how to use them to distinguish universes with identical local geometry that differ only in their topology. Furthermore, we will see that if the spacetime topology induces a preferred direction, vacuum entanglement harvesting becomes sensitive to it, thus pointing out a connection between spacetime topology, vacuum fluctuations, and the field vacuum entanglement structure.
Quantum correlated probes have the potential of delivering enhanced precision in estimating individual parameters. Obtaining quantum enhancements in scenarios of wider appeal such as imaging require an understanding of the quantum limits of estimating several parameters across multiple modes simultaneously. The problem is made theoretically and well as practically interesting and non-trivial by the possible non-commutativity of the optimal measurements needed to attain the quantum limits for estimating individual parameters. We present developments on the quantum theory of estimating multiple parameters -- arising from both unitary dynamics as well as decoherence -- simultaneously in a few scenarios, and its ramifications in the imaging of real-world samples.