  The emerging quantum technologies rely on our ability to establish and
control quantum systems in nonclassical states, exhibiting entanglement and
quantum coherence. It is thus crucial to understand how entanglement and
coherence can be created in the most efficient way. In this work we study
optimal ways to create a large amount of quantum coherence via quantum
channels. For this, we compare different scenarios, where the channel is acting
on an incoherent state, on states which have coherence, and also on subsystems
of multipartite quantum states. We show that correlations in multipartite
systems do not enhance the ability of a quantum channel to create coherence. We
also study the ability of quantum channels to destroy coherence, proving that a
channel can destroy more coherence when acting on a subsystem of a bipartite
state. Crucially, we also show that the destroyed coherence on multipartite
system can exceed the upper bound of those on the single system when the total
state is entangled. Our results significantly simplify the evaluation of
coherence generating capacity of quantum channels, which we also discuss.
