  In the history of quantum mechanics, various types of uncertainty
relationships have been introduced to accommodate different operational
meanings of Heisenberg uncertainty principle. We derive an optimized entropic
uncertainty relation (EUR) that quantifies an amount of quantum uncertainty in
the scenario of successive measurements. The EUR characterizes the limitation
in the measurability of two different quantities of a quantum state when they
are measured through successive measurements. We find that the bound quantifies
the information between the two measurements and imposes a condition that is
consistent with the recently-derived error-disturbance relationship.
