  Recently, an entropic uncertainty relation for multiple measurements has been
proposed by Liu et al. in [Phys. Rev. A 91, 042133 (2015)]. However, the lower
bound of the relation is not always tight with respect to different
measurements. Herein, we improve the lower bound of the entropic uncertainty
relation for multiple measurements, termed as simply constructed bound (SCB).
We verify that the SCB is tighter than Liu et al.'s result for arbitrary
mutually unbiased basis measurements, which might play a fundamental and
crucial role in practical quantum information processing. Moreover, we optimize
the SCB by considering mutual information and the Holevo quantity, and propose
an optimized SCB (OSCB). Notably, the proposed bounds are extrapolations of the
behavior of two measurements to a larger collection of measurements. It is
believed that our findings would shed light on entropy-based uncertainty
relations in the multiple measurement scenario and will be beneficial for
security analysis in quantum key distributions.
