  Quantifying coherence is a key task in both quantum mechanical theory and
practical applications. Here, a reliable quantum coherence measure is presented
by utilizing the quantum skew information of the state of interest subject to a
certain broken observable. This coherence measure is proven to fulfill all the
criteria (especially the strong monotonicity) recently introduced in the
resource theories of quantum coherence. The coherence measure has an analytic
expression and an obvious operational meaning related to quantum metrology. In
terms of this coherence measure, the distribution of the quantum coherence,
i.e., how the quantum coherence is distributed among the multiple parties is
studied and a corresponding polygamy relation is proposed. As a further
application, it is found that the coherence measure forms the natural upper
bounds for quantum correlations prepared by incoherent operations. The
experimental measurement of our coherence measure as well as the
relative-entropy coherence, $l_p$-norm coherence is studied finally.
