Has any quantum mechanics experiment ever suggested the past or future could be changed? This question has already been asked in many guises but unfortunately all the responses run the gamut of possible answers with no one who appears to be in agreement therefore I will ask in a slightly different angle everyone will appreciate. First the motivation for this question lies simply in the overwhelming news in the popular press concerning QM and some of the claims appear to be somewhat outlandish to a hobbyist as myself. Simply has any QM experiment ever confirmed, predicted or suggested that an established past event has been changed in the past or the future and demonstrated by the experiment?  By the very definition of past and future it seems to be a logical paradox but I will spare those details and say that these claims appear to be popular in today's science news. Thank You.
 A: I can see only two ways to interpret this question, and each leads to a trivial answer.
If you are asking whether the spacetime we live in could be different and still be the spacetime we live in, the answer is no because two things that are different cannot be the same.
If you are asking whether there could be another spacetime that is very similar to ours but differs only in some small details, the answer seems very likely to be yes, though it's conceivable that for some odd currently unimagined reason, every spacetime that is sufficiently similar to ours must be identical to ours.
If you are asking something else, then I have no idea what you are asking.
A: Before I go a bit out on a limb, I will say that from an operational perspective that the answer Anna V gave is pretty good. It basically says that quantum physics from an experimental view computes amplitudes that give probabilities for measurements to be made in the future. 
The arrow of time and the apparent change in entropy $dS/dt~\ge~0$ is with coarse grained or thermal entropy. We may think of the fine grained entropy for two entangled systems as $S(A\cup B)~=~S(A)~+~S(B)~-~S(A|B)$, which is related to the coarse grained entropy if we remove the $S(A|B)$. What that tells us then is that coarse grained entropy occurs when we lack the fine grained details of where entanglement phase of $A$ and $B$ is transferred or exchanged to an open world in ways not known. We may then related that to a reduced quantum state, which involves a change of entropy, and something which occurs in the future. We have connection still with Anna's comment.
Now suppose we have a coset space/group system for entanglements. A symplectic or symplectic-unitary group $\cal G$ defines a system modulo equivalent group transformations or gauge connection on a section $X$, and so $\Xi~=~{\cal G}/X$ is a symmetry of entanglement. If this has noetherian properties then it predicts conservation of qubits. This means that a measurement or thermal change $\Delta S~\ge~0$ is a measure of ignorance on how entanglement phase is exchanged, but qubits are still conserved. Hence outcomes are still something in the future.
This is a subjective definition of time based on the subjective definition of thermal entropy. If it is subjective, then can it be reversed? Sort of, and some experiments with systems with small number of particles can have $\Delta S~<~0$ at least in a transient time period. However, on the large let us suppose that we could reverse this apparent loss of entanglement phase so rather than being lost in the future it appears in the past. Quantum mechanics as a time symmetric theory tells us nothing whether one is true or false. So if entanglement phase in a coarse grained sense did appear in the past, opposite our standard definition, then in a sense all we have really done is to place a minus sign to our definition of time. Nothing has actually changed!
In a multiverse setting it is entirely possible that different cosmologies have different arrows of time relative to each other. However, if you were an observer in a cosmology with an arrow of time opposite to our you would observe nothing at all different. Time would still appear to be in one direction.
A: 
Simply has any QM experiment ever confirmed, predicted or suggested that an established past event has been changed in the past or the future and demonstrated by the experiment?

Quantum mechanical predictions for experimental setups always have to do with the arrow of time, the prediction is for a future measurement. Past events by construction cannot be changed and future events can, by changing the boundary conditions. The predictions are probabilistic, but that is another story.
