Bounds on Capacity and Power of Quantum Batteries.

Quantum batteries, composed of quantum-cells, are expected to outperform their classical analogs. The origin of such advantages lies in the role of quantum correlations, which may arise during the charging and discharging processes performed on the battery. In this work, we introduce a systematic characterization of the relevant quantities of quantum batteries, i.e., capacity and power, in relation to such correlations. For these quantities, we derive tighter bounds for batteries that are a collection of non-interacting quantum-cells with fixed Hamiltonians. The bound on capacity is derived with the help of the energy-entropy diagram, and this bound is respected as long as the charging and discharging processes are entropy preserving. While studying power, we consider a geometric approach for the evolution of the battery state in the energy eigenspace of the battery Hamiltonian. Then, a tighter bound on power is derived for arbitrary charging process, in terms of the Fisher information and the energy fluctuation of the battery. The former quantifies the speed of evolution, and the latter encodes non-local character of the battery state. We discuss paradigmatic models for batteries that saturate the bounds both for the capacity and the power. Several physically realizable batteries, based on integrable spin chains, Lipkin-Meshkov-Glick model and Dicke model, are also studied in the light of these newly introduced bounds.