Abstract: The speed of quantum evolution is bounded by the quantum speed limits (QSLs) which may be formulated in terms of properties of the driving Hamiltonian (in particular, its variance). QSLs will be introduced and used to motivate the study of quantum power. Defining the notion of a quantum battery the question of achieving high driving power is then phrased in terms of powerful battery charging. For the simplest possible model of a quantum battery -- a work qubit (or 'wit') -- an optimal charging protocol may be derived. Extending the analysis to an array of N qubits, it is demonstrated that an N-fold advantage in power per wit can be achieved when global operations are permitted (rather than a restriction to local operations and classical communication (LOCC)). Interestingly, this quantum advantage for power holds even when, with cyclic operation in mind, initial and final states are required to be separable. The exemplary analytic argument for this quantum advantage in the charging power is explained by a geometric argument on the one side and a re-consideration of the applicable quantum speed limit on the other.
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