  It is said about quantum interference that "In reality, it contains the only
mystery". Indeed, together with non-locality it is often considered as the
characteristic feature of quantum theory which can not be explained in any
classical way. In this work we are concerned with a restricted setting of a
single particle propagating in multi-path interferometric circuits, that is
physical realisation of a qudit. It is shown that this framework, including
collapse of the wave function, can be simulated with classical resources
without violating the locality principle. We present a local ontological model
whose predictions are indistinguishable from the quantum case. 'Non-locality'
in the model appears merely as an epistemic effect arising on the level of
description by agents whose knowledge is incomplete. This result suggests that
the real quantum mystery should be sought in the multi-particle behaviour,
since single-particle interferometric phenomena are explicable in a classical
manner.
