Managing quantum energetic resources in noisy environments

In this Thesis we build two conceptual frameworks to understand how we can manage energy in the quantum regime, and we propose schemes to fight noise in quantum batteries. We start by reviewing the basic knowledge about quantum states and quantum channel. Then, we discuss the basic the concept of work extraction in Quantum Mechanics. After that, we give a brief exposition of Gaussian states and Gaussian channels.Following that, we introduce the concept of quantum energy lines (QELs), which allow us to formally define the problem of transporting energy for quantum purposes. We give some examples of QELs in the form of bosonic Gaussian channels (BGCs), and we prove that the best states to fight noise for a large subclass of BGCs are the coherent states. To prove this fact, we maximize various quantum work extraction functionals, such as the ergotropy, over the input state after the noise has affected the system.Then, we study a model of QEL which is a semi-classical generalization of the model of Kelly betting of repeated bets, where we identify value with ergotropy. Here, the bet is a random application of a BGC. We prove that coherent states obtain the maximum ergotropy gain and we obtain an analogous of the formula for the Kelly criterion in this context.After that, We delve deeper in the theory of work-functional maximization by defining the quantum work capacitances and the maximal asymptotic work/energy ratio (MAWER). We prove that these figure of merit can certify the capability of a quantum battery to sustain environmental noise.With these theoretical tools we study the effect of non-local resources in energy preservation. Specifically, we find that the non-locality is useless, if the work-extracting operations are local. While, it is indispensable in energy extraction.We then compute the quantum work capacitances and the MAWER of various noise models. In the case of self-discharging in contact with a thermal environment, we prove that quantum coherence may enhance the capability of a battery to fight noise, showing a genuine quantum advantage in this context.Finally, we propose an experimental platform for a realistic quantum battery in contact with an electromagnetic environment. We analyze two different arrangements of a one-dimensional waveguide-QED system: an ordered and a disordered array. We prove the both configurations outperform the single-atom benchmark, showing how collective effects may enhance energy storage performances.