  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 theoretical work, we introduce a
systematic characterization of the relevant quantities of quantum batteries,
i.e., the capacity and the power, in relation to such correlations. For these
quantities, we derive upper bounds for batteries that are a collection of
noninteracting quantum cells with fixed Hamiltonians. The capacity, that is, a
bound on the stored or extractable energy, 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, an upper bound for power is
derived for arbitrary charging process, in terms of the Fisher information and
the energy variance of the battery. The former quantifies the speed of
evolution, and the latter encodes the nonlocal character of the battery state.
Indeed, due to the fact that the energy variance is bounded by the multipartite
entanglement properties of batteries composed of qubits, we establish a
fundamental bound on power imposed by quantum entanglement. We also discuss
paradigmatic models for batteries that saturate the bounds both for the stored
energy and power. Several experimentally realizable quantum batteries, based on
integrable spin chains, the Lipkin-Meshkov-Glick and the Dicke models, are also
studied in the light of these newly introduced bounds.
