  Detecting multipartite quantum coherence usually requires quantum state
reconstruction, which is quite inefficient for large-scale quantum systems.
Along this line of research, several efficient procedures have been proposed to
detect multipartite quantum coherence without quantum state reconstruction,
among which the spectrum-estimation-based method is suitable for various
coherence measures. Here, we first generalize the spectrum-estimation-based
method for the geometric measure of coherence. Then, we investigate the
tightness of the estimated lower bound of various coherence measures, including
the geometric measure of coherence, $l_1$-norm of coherence, the robustness of
coherence, and some convex roof quantifiers of coherence multiqubit GHZ states
and linear cluster states. Finally, we demonstrate the
spectrum-estimation-based method as well as the other two efficient methods by
using the same experimental data [Ding et al. Phys. Rev. Research 3, 023228
(2021)]. We observe that the spectrum-estimation-based method outperforms other
methods in various coherence measures, which significantly enhances the
accuracy of estimation.
