  The distribution of quantum coherence in multipartite systems is one of the
basic problems in the resource theory of coherence. While the usual coherence
measures are defined on a single system and cannot capture the nonlocal
correlation between subsystems, in order to deal with the distribution of
coherence it is crucial to quantify the coherence in bipartite systems
properly. Here, we introduce incoherent-quantum (IQ) coherence measures on
bipartite systems, which can characterize the correlations between systems.
According to the IQ coherence measures on bipartite systems, we find the
distribution of coherence of formation and assistance in bipartite systems: the
total coherence of formation is lower bounded by the sum of coherence of
formation in each subsystem and the entanglement of formation between the
subsystems, while the total coherence of assistance is upper bounded by the sum
of coherence of assistance in each subsystem and the entanglement of assistance
between subsystems. Besides, we also obtain the tradeoff relation between the
coherence cost and entanglement cost, distillable coherence and distillable
entanglement in bipartite systems. Thus, the IQ coherence measures introduced
here truly capture the nonlocal correlation between subsystems and reveal the
distribution of coherence in bipartite systems.
