  We derive a trade-off relation between the accuracy of implementing a desired
unitary evolution using a restricted set of free unitaries and the size of the
assisting system, in terms of the resource generating/losing capacity of the
target unitary. In particular, this relation implies that, for any theory
equipped with a resource measure satisfying lenient conditions, any resource
changing unitary cannot be perfectly implemented by a free unitary applied to a
system and an environment if the environment has finite dimensions. Our results
are applicable to a wide class of resources including energy, asymmetry,
coherence, entanglement, and magic, imposing ultimate limitations inherent in
such important physical settings, as well as providing insights into
operational restrictions in general resource theories.
