Control and complexity in quantum statistical mechanics

Developing a comprehensive theory of thermodynamics at the quantum scale requires a fundamental change of perspective with regards to its classical counterpart. On the one hand, measuring a quantum system will induce a non-negligible back-action and an energy cost that is at least comparable to the energy scale of the system. On the other hand, controlling microscopic degrees of freedom and harnessing quantum effects provides novel opportunities with no classical counterpart. In light of these facts, control over different quantum features and quantum measurements themselves become valuable resources that need to be integrated into any self-contained theory of quantum thermodynamics. In this project, we aim to address this grand challenge. First we will develop a formal theory that includes control over quantum systems with fixed complexity to incorporate these concepts into thermodynamic considerations at the quantum scale. Second, we will unveil the fundamental thermodynamic limitations on information acquisition by constructing a thermodynamically self-contained description of the quantum measurement process. Finally, we will carefully study current quantum technologies and, with the help of our own lab and experimental colleagues, we will devise experimental proposals and perform proof-of-principle experiments based on existing quantum technologies, to make sure that the theoretical considerations describe relevant features.