Uncertainty relations for unified ($\alpha$,$\beta$)-relative entropy of coherence under mutually unbiased equiangular tight frames

Uncertainty relations based on quantum coherence is an important problem in quantum information science. We discuss uncertainty relations for averaged unified ($\alpha$,$\beta$)-relative entropy of coherence under mutually unbiased equiangular tight frames, and derive an interesting result for different parameters. As consequences, we obtain corresponding results under mutually unbiased bases, equiangular tight frames or based on Tsallis $\alpha$- relative entropies and R\'enyi-$\alpha$ relative entropies. We illustrate the derived inequalities by explicit examples in two dimensional spaces, showing that the lower bounds can be regarded as good approximations to averaged coherence quantifiers under certain circumstances.