Optimized entropic uncertainty relations for multiple measurements

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