  It is well known that in Anderson localized systems, starting from a random
product state the entanglement entropy remains bounded at all times. However,
we show that adding a single boundary term to an Anderson localized Hamiltonian
leads to unbounded growth of entanglement. Our results imply that Anderson
localization is not a local property. One cannot conclude that a subsystem has
Anderson localized behavior without looking at the whole system, as a term that
is arbitrarily far from the subsystem can affect the dynamics of the subsystem
in such a way that the features of Anderson localization are lost.
