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

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