  The concept of quantum coherence, including various ways to quantify the
degree of coherence with respect to the prescribed basis, is currently the
subject of active research. The complementarity of quantum coherence in
different bases was studied by deriving upper bounds on the sum of the
corresponding measures. To obtain a two-sided estimate, lower bounds on the
coherence quantifiers are also of interest. Such bounds are naturally referred
to as uncertainty relations for quantum coherence. We obtain new uncertainty
relations for coherence quantifiers averaged with respect to a set of mutually
unbiased bases (MUBs). To quantify the degree of coherence, the relative
entropy of coherence and the geometric coherence are used. Further, we also
derive novel state-independent uncertainty relations for a set of MUBs in terms
of the min-entropy.
