  A classical random walker starting on a node of a finite graph will always
reach any other node since the search is ergodic, namely it is fully exploring
space, hence the arrival probability is unity. For quantum walks, destructive
interference may induce effectively non-ergodic features in such search
processes. Under repeated projective local measurements, made on a target
state, the final detection of the system is not guaranteed since the Hilbert
space is split into a bright subspace and an orthogonal dark one. Using this we
find an uncertainty relation for the deviations of the detection probability
from its classical counterpart, in terms of the energy fluctuations.
