Distribution of coherence in bipartite systems based on incoherent-quantum coherence measures

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.