Work Functionals for Thermalising Quantum Maps

It is now experimentally established that utilising quantum effects in battery charging processes leads to a measurable advantage in terms of charging speed. However, environmental noise can negatively impact energy recovery efficiency from the battery. In this context, Work Capacitances (WCaps) play a crucial role in quantifying robustness against noise in work extraction processes performed on collections of quantum systems (i.e., quantum batteries). WCaps allow for easier comparison of performances across different experimental platforms and provide theoretical bounds on the amount of work an agent can extract from a quantum battery. Moreover, the knowledge of the WCaps associated with a specific experimental implementation could aid in developing optimal energy encoding strategies, thereby reducing energy dissipation caused by noise. WCaps depend on the chosen work functional, and among various options, ergotropy is undoubtedly the most fundamental. Following the modern interest in high-dimensional quantum systems for computation, in this work various ergotropic quantities are evaluated for qudits, and in particular qutrits, under the influence of different noise models. Specifically, self-discharging (Multilevel Amplitude Damping channel, in short MAD) is analysed first, and some of its general properties are demonstrated. In addition to numerical results, the analytical form of ergotropy is obtained using computer-assisted symbolic calculations for specific noise parameter values. Subsequently, the obtained results regarding ergotropy concavity are used to determine some of the ergotropic capacitances of the channels within specific parameter intervals. Next, aiming to model a more realistic scenario, a number of channels which describe the interaction of the system with a bath of non-zero temperature are introduced, and their ergotropy characterised; finally, one of the presented channels is proposed as a faithful generalisation of the MAD channel to non-zero bath temperature (Generalised Multilevel Amplitude Damping channel, GMAD).