  We give a simple proof of the uncertainty principle with quantum side
information, as in [Berta et al. Nature Physics 6, 659 (2010)], invoking the
monotonicity of the relative entropy. Our proof shows that the entropic
uncertainty principle can be viewed as a data-processing inequality, a special
case of the notion that information cannot increase due to evolution in time.
This leads to a systematic method for finding the minimum uncertainty states of
various entropic uncertainty relations; interestingly such states are
intimately connected with the reversibility of time evolution.
