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Coherence is the most fundamental quantum feature in quantum mechanics. For abipartite quantum state, if a measurement is performed on one party, the otherparty, based on the measurement outcomes, will collapse to a correspondingstate with some probability and hence gain the average coherence. It is shownthat the average coherence is not less than the coherence of its reduceddensity matrix. In particular, it is very surprising that the extra averagecoherence (and the maximal extra average coherence with all the possiblemeasurements taken into account) is upper bounded by the classical correlationof the bipartite state instead of the quantum correlation. We also find thesufficient and necessary condition for the null maximal extra averagecoherence. Some examples demonstrate the relation and, moreover, show thatquantum correlation is neither sufficient nor necessary for the nonzero extraaverage coherence within a given measurement. In addition, the similarconclusions are drawn for both the basis-dependent and the basis-free coherencemeasure.

The classical correlation limits the ability of the measurement-induced average coherence