Is time only a macroscopic property?

Imagine a quantum mechanical wave function. First you measure its position. Clearly the collapse of this wave function into a defined position state is a move forward in time. But when you continue to measure its momentum, by the uncertainty principle any information about its position is lost. So the wave function is completely reset. From the point of view of the wave function this is indistinguishable from time travel. It is as if the wave function has travelled along a closed timelike curve.

Thoughts, /sci/? Could we make time travel possible by using the right sequence of QM observables?