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Quantifying coherence is a key task in both quantum mechanical theory andpractical applications. Here, a reliable quantum coherence measure is presentedby utilizing the quantum skew information of the state of interest subject to acertain broken observable. This coherence measure is proven to fulfill all thecriteria (especially the strong monotonicity) recently introduced in theresource theories of quantum coherence. The coherence measure has an analyticexpression and an obvious operational meaning related to quantum metrology. Interms of this coherence measure, the distribution of the quantum coherence,i.e., how the quantum coherence is distributed among the multiple parties isstudied and a corresponding polygamy relation is proposed. As a furtherapplication, it is found that the coherence measure forms the natural upperbounds for quantum correlations prepared by incoherent operations. Theexperimental measurement of our coherence measure as well as therelative-entropy coherence, $l_p$-norm coherence is studied finally.

Quantum Coherence via Skew Information and Its Polygamy