  The uncertainty principle limits quantum states such that when one observable
takes predictable values there must be some other mutually unbiased observables
which take uniformly random values. We show that this restrictive condition
plays a positive role as the enabler of non-classical dynamics in an
interferometer. First we note that instantaneous action at a distance between
different paths of an interferometer should not be possible. We show that for
general probabilistic theories this heavily curtails the non-classical
dynamics. We prove that there is a trade-off with the uncertainty principle,
that allows theories to evade this restriction. On one extreme, non-classical
theories with maximal certainty have their non-classical dynamics absolutely
restricted to only the identity operation. On the other extreme, quantum theory
minimises certainty in return for maximal non-classical dynamics.

Quantum Physics