  The distribution of coherence in multipartite systems is one of the
fundamental problems in the resource theory of coherence. To quantify the
coherence in multipartite systems more precisely, we introduce new coherence
measures, incoherent-quantum (IQ) coherence measures, on bipartite systems by
the max- and min- relative entropies and provide the operational interpretation
in certain subchannel discrimination problem. By introducing the smooth max-
and min- relative entropies of incoherent-quantum (IQ) coherence on bipartite
systems, we exhibit the distribution of coherence in multipartite systems: the
total coherence is lower bounded by the sum of local coherence and genuine
multipartite entanglement. Besides, we find the monogamy relationship for
coherence on multipartite systems by incoherent-quantum (IQ) coherence
measures. Thus, the IQ coherence measures introduced here truly capture the
non-sharability of quantumness of coherence in multipartite context.
