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In conventional measurement, to reach the greatest accuracy of parameterestimation, all samples must be measured since each independent sample containsthe same quantum Fisher information. In postselected metrology, postselectioncan concentrate the quantum Fisher information of the initial samples into atiny post-selected sub-ensemble. It has been proven that this quantum advantagecan not be realized in any classically commuting theory. In this work, wepresent that the advantage of postselection in weak value amplification (WVA)can not be achieved without quantum coherence. The quantum coherence of theinitial system is closely related to the preparation costs and measurementcosts in parameter estimation. With the increase of initial quantum coherence,the joint values of preparation costs and measurement costs can be optimized tosmaller. Moreover, we derive an analytical tradeoff relation between thepreparation, measurement and the quantum coherence. We further experimentallytest the tradeoff relation in a linear optical setup. The experimental andtheoretical results are in good agreement and show that the quantum coherenceplays a key role in bounding the resource costs in the postselected metrologyprocess.

Advantage of quantum coherence in postselected metrology