  We introduce a universal scheme to divide the power output of a periodically
driven quantum heat engine into a classical contribution and one stemming
solely from quantum coherence. Specializing to Lindblad-dynamics and small
driving amplitudes, we derive general upper bounds on both, the coherent and
the total power. These constraints imply that, in the linear-response regime,
coherence inevitably leads to power losses. To illustrate our general analysis,
we explicitly work out the experimentally relevant example of a single-qubit
engine.
