  Detecting multipartite quantum coherence usually requires quantum state
reconstruction, which is quite inefficient for large-scale quantum systems.
Here, we show that the spectrum-estimation-based method is capable of detecting
multipartite quantum coherence of various coherence measures efficiently. With
the spectrum-estimation-based method, we observe that the lower bound of
coherence is significantly enhanced than the fidelity-based estimation method
in measures of the coherence of formation and the geometric measure of
coherence, as well as the witness-based estimation method in the measure of the
robustness of coherence. We test our scheme using the existing experimental
data [Ding et al. arXiv:2010.02612 (2020)].
