Exploiting symmetry and criticality in quantum sensing and quantum simulation

Decoherence and errors appear among the main challenges to implement successful quantum technologies. In this thesis I discuss the application of some general tools and principles that may be valuable resources to develop robust technologies, with applications in quantum sensing and quantum simulation. Firstly, we employ suitable periodically driving fields acting on the Ising model in order to tailor spin-spin interactions depending on the spatial direction of the bonds. In this way, we are able to simulate the quantum compass model on a square lattice. This system exhibits topological order and a doubly degenerate ground state protected against local noise. A possible implementation of this proposal is outlined for atomic quantum simulators. Secondly, we exploit two general working principles based on spontaneous symmetry breaking and criticality that may be beneficial to achieve robust quantum sensors, particularly appropriate for quantum optical dissipative systems. A concrete application is given for a minimal model: a single qubit laser. It is shown how the precision in parameter estimation is enhanced as the incoherent pumping acting on the qubit increases, and also when the system is close to the lasing critical point. Finally, classical long-range correlations in lattice systems are shown to provide us with an additional resource to be used in robust sensing schemes. The previous setup is extended to a lattice of single qubit lasers where interactions are incoherent. Under the right conditions, we show that a Heisenberg scaling with the number of probes can be accomplished.