  Uncertainty and disturbance are two most fundamental properties of a quantum
measurement and they are usually separately studied in terms of the preparation
and the measurement uncertainty relations. Here we shall establish an intimate
connection between them that goes beyond the above mentioned two kinds of
uncertainty relations. Our basic observation is that the disturbance of one
measurement to a subsequent measurement, which can be quantified based on
observed data, sets lower-bounds to uncertainty. This idea can be universally
applied to various measures of uncertainty and disturbance, with the help of
data processing inequality. The obtained relations, referred to as disturbance
enhanced uncertainty relations, immediately find various applications in the
field of quantum information. They ensure preparation uncertainty relation such
as novel entropic uncertainty relations independent of the Maassen and Uffink
relation. And they also result in a simple protocol to estimate coherence. We
anticipate that this new twist on uncertainty principle may shed new light on
quantum foundations and may also inspire further applications in the field of
quantum information.
