Average coherence with respect to complementary measurements

Abstract: We investigate the average coherence with respect to a complete set of complementary measurements. By using a Wigner-Yanase skew information-based coherence measure introduced in [Phys. Rev. A \textbf{96}, 022130, 2017], we evaluate the average coherence of a state with respect to any complete set of mutually unbiased measurements and general symmetric informationally complete measurements, respectively. We also establish analytically the relations among these average coherences.