Is there experimental evidence for the irreversibility of the collapse of the state of a system due to a measurement? It has been pointed out by one of my professors that, in quantum mechanics, 

the collapse of the state of the system by measurement is not
  time-reversible, i.e once the system collapses due to a measurement,
  we cannot reverse that process.

However, I'm wondering is that any experimental evidence for such a claim.
I mean if we don't have any method to do such a reversibility, this means that we don't know, for the time being, whether such a process possible; however, since he specifically mentioned as "irreversible", 
Question:
Is there experimental evidence for the irreversibility of the collapse of the state of a system due to a measurement ?
 A: There can be no evidence for the "irreversibility of collapse" because "collapse" is a feature that an interpretation of quantum mechanics may or may not possess, cf. e.g. the overview table at Wikipedia. Interpretations are ontologies/stories that are imposed on top of the raw formalism and generally do not change its predictions, i.e. are experimentally indistinguishable.
However, on a formal level, the "irreversibility of collapse" is simply the fact that collapse would have to be represented by some sort of projector onto a subset of eigenspaces of the observable being measured, and projectors are operators that have no inverse (because they have zero eigenvalues), hence the operator they represent is not reversible. You don't need evidence for this mathematical fact, the question is simply whether the interpretation of quantum mechanics you adhere to says that this sort of projection is an actual step that occurs during measurement or not. That is, the question about "reality" that you should ask is not whether collapse is reversible, but whether it occurs at all.
A: As far as I know, there is no experimental evidence of such irreversibility or collapse itself. In this respect, I often quote the following review of experimental data (M. Schlosshauer, Annals of Physics, 321 (2006) 112-149):
""(i) the universal validity of unitary dynamics and the superposition principle has been confirmed far into the mesoscopic and macroscopic realm in all experiments conducted thus far;
(ii) all observed ‘‘restrictions’’ can be correctly and completely accounted for by taking into account environmental decoherence effects;
(iii) no positive experimental evidence exists for physical state-vector collapse;" 
