  We introduce and study the task of assisted coherence distillation. This task
arises naturally in bipartite systems where both parties work together to
generate the maximal possible coherence on one of the subsystems. Only
incoherent operations are allowed on the target system while general local
quantum operations are permitted on the other, an operational paradigm that we
call local quantum-incoherent operations and classical communication (LQICC).
We show that the asymptotic rate of assisted coherence distillation for pure
states is equal to the coherence of assistance, an analog of the entanglement
of assistance, whose properties we characterize. Our findings imply a novel
interpretation of the von Neumann entropy: it quantifies the maximum amount of
extra quantum coherence a system can gain when receiving assistance from a
collaborative party. Our results are generalized to coherence localization in a
multipartite setting and possible applications are discussed.
