  Constraints on work extraction are fundamental to our operational
understanding of the thermodynamics of both classical and quantum systems. In
the quantum setting, finite-time control operations typically generate
coherence in the instantaneous energy eigenbasis of the dynamical system.
Thermodynamic cycles can, in principle, be designed to extract work from this
non-equilibrium resource. Here, we isolate and study the quantum coherent
component to the work yield in such protocols. Specifically, we identify a
coherent contribution to the ergotropy (the maximum amount of unitarily
extractable work via cyclical variation of Hamiltonian parameters). We show
this by dividing the optimal transformation into an incoherent operation and a
coherence extraction cycle. We obtain bounds for both the coherent and
incoherent parts of the extractable work and discuss their saturation in
specific settings. Our results are illustrated with several examples, including
finite-dimensional systems and bosonic Gaussian states that describe recent
experiments on quantum heat engines with a quantized load.
