Ozgen Eren, we've already had a fairly extended discussion of quantum randomness in this thread:
https://www.physicsforums.com/threads/a-very-basic-question-about-heisenberg-uncertainty.786473/
There's not much point in rehashing that discussion again; you're going to get the same answers here that you did in the other thread.
Ozgen Eren said:
Where are the most significant ones are published?
Try Googling these for a start: double slit experiment, Stern-Gerlach experiment (this is probably the simplest one, I'll discuss it a bit below), Airy experiment, Aspect experiment (the last one was a test of Bell's Theorem so it shows nonlocality, not just randomness).
The basic fact is that you can take a bunch of quantum systems that were all prepared in exactly the same way, put them through exactly the same experimental apparatus, and get different results. For example, in the Stern-Gerlach experiment, they took a bunch of electrons (actually they were silver atoms with one electron having its spin unpaired in the original, I believe it's now been redone with single electrons) which had all been prepared in exactly the same way (I'll go into that a bit more below), and put them through the same magnetic field. The electrons came out in two beams, which we can call "up" and "down". All the electrons were identical going in, yet they came out in two beams. That's quantum randomness.
Now you might zero in on that "prepared the same way" bit, because how can we know for sure that the electrons really were identical going in? Maybe there were some slight differences (the usual term in the QM literature is "hidden variables") that were too small for us to measure beforehand but which caused the electrons to split into two beams. In this particular case, the obvious "hidden variable" is the precise direction of the electron's spin axis. (Note that even on this view, the classical prediction for what should happen was still wrong: classical EM predicted that the electrons should come out in a whole range of directions, with a peak in the middle, depending on the exact orientation of the electron's spin relative to the magnetic field. There is no way to get a prediction of two separate beams from classical EM. So something has to change; the question is what.)
However, we can eliminate the above factor too, by simply
forcing all the electrons going into have exactly the same spin orientation. The simplest way to do that is to take the electrons from one output beam of a previous Stern-Gerlach device, oriented in a different direction, for example left-right instead of up-down. All the electrons in the left output beam of this device have their spins pointing to the left--and we can verify this by passing them all through a second left-right Stern-Gerlach device and seeing that they all come out in a single beam, the left beam. In other words, we can execute a preparation procedure for the electrons that, by a simple test, gives us a beam of electrons that are, indeed, identical, because we can test them to be identical by re-running the preparation procedure on them and seeing that it leaves them unchanged.
And yet, even then, if we take this beam of spin-left electrons and put it through a Stern-Gerlach device oriented up-down,
we still get two output beams, an up beam and a down beam.
That is quantum randomness.