  Quantum walks are counterparts of classical random walks. They spread faster,
which can be exploited in information processing tasks, and constitute a
versatile simulation platform for many quantum systems. Yet, some of their
properties can be emulated with classical light. This rises a question: which
aspects of the model are truly nonclassical? We address it by carrying out a
photonic experiment based on a pre- and post-selection paradox. The paradox
implies that if somebody could choose to ask, either if the particle is at
position x = 0 at even time steps, or at position x = d (d > 1) at odd time
steps, the answer would be positive, no matter the question asked. Therefore,
the particle seems to undergo long distance oscillations despite the fact that
the model allows to jump one position at a time. We translate this paradox into
a Bell-like inequality and experimentally confirm its violation up to eight
standard deviations.
