In this thesis, we study the optimization of operational tasks that involve the manipulation of quantum resources. In most cases, such optimizations are aided by understanding the geometric properties of the physical objects involved. We split our results in a first part concerning Thermodynamics, and a second part concerning Information Theory. 

In the context of Thermodynamics, we first study the optimization of thermal machines. That is, we look for those periodic control protocols, performed on a quantum working fluid, that maximize figures of merit based on power and efficiency. By making small assumptions on the dynamical regimes (of low-dissipation/slow-driving, or fast-driving), we are able to construct and characterize optimal protocols that are valid for large classes of quantum (and classical) thermal machines.

Secondly, we study how to design quantum thermal probes that optimize the precision in temperature estimation when put in contact with a thermal bath. The resulting optimal configurations are simple and physically feasible, and show an Heisenberg-like scaling of the optimal sensitivity.

In the context of Information Theory, initially we study how to characterize memory effects (information backflows) in the dynamics of open quantum systems, how to detect them and operationally exploit them.

Furthermore, in the subfield of Nonlocality, we study relaxations and generalisation of the canonical Bell scenario, which allow us to bring the realization of nonlocal experiments closer to simple, table-top quantum optics. In particular, by considering nonlocality in quantum networks, we are able to design an experiment which only involves simple passive optics and single-photon entangled states, in which it is possible to certify nonlocality without measurement inputs. Likewise, a different relaxation consists in allowing trusted quantum inputs in a Bell experiment. This permits certifying nonlocality of any entangled state, without trusting the measurement device. We study this measurement-device-independent framework to design simple protocols of entanglement detection for continuous-variable states.

The results of the thesis are relevant both from the theoretical point of view and for the efficient realisation of the operational tasks analysed.

Thesis Director:  ICREA Prof Dr Antonio Acín