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

Distribution of coherence in multipartite systems under entropic coherence measure