Even if the alien does not create a perfect copy of the quantum state, we will not know.
First, 99.99% of all people (possibly more) couldn't tell anyway if the copy wasn't quantum perfect. As long as the copy is perfect within maybe millimeter scale or so (say pico if you will), few will observe it at all, of those only few will notice, and of those who do, most will do it away.
Second, from inside a system, there is no way we could tell "truth" anyway. In order to notice that something has changed, we would have to have access to external information. That's true for every system. Luckily there's an entire universe around us, isn't there! While that solves the problem in theory, in practice things are much different.
Easily observed, or not that easily observed details such as the sun being not in sync with every clock on the planet, or stars "jumping" in the sky, or deep space radio signals having a hitch will not do.
Humans are excellent at denying truth, and they are even better at coming up with a plausible explanation when their beliefs are shaken. In fact, that's probably what humans are best at.
I've recently had the opportunity to observe this on a person with ischemic stroke. That person was motorically 100% functional, but cognitively entirely dysfunct. He had his tablet computer in his hands and was typing random characters and approx. 200 emotes (whatever the onscreen keyboard creates when you keep tapping randomly) into the email program's
To: field (no network access, mind you). The person was deeply convinced of knowing what he was doing, and it was an important task (without being able to tell what).
A week and half later, that same person was, again, fully functional. Still, even today, he denies the externally observable truth, insisting on having done something orderly, and important (without being able to tell what). Is that man a liar? Well no. From his point of view, from what's stored inside his brain, that is indeed the exact truth. Even if you showed to him a video recording of what happened, then this couldn't be true. Because, well, that's obviously not what happened, the video must be fake.
Remember the famous garbage-guy scene from the "Voyage Home" Star Trek movie:
(strong wind, a garbage can gets flattened, a hatch opens out of nowhere, weird people come out of it, hatch closes and is gone)
Did you see that?!!
No. And neither did you, so shut up.
Worded differently, if your clock is wrong, then you should probably adjust it. If you just saw the stars jump in the sky, then you should igore it, or maybe see a neurologist. If the guy next do you saw the same thing, it's folie à deux. Or it was a reflection of, something that flew by. Weather balloon?
If the government's clocks are all wrong, then some stupid bureaucrat fucked it up. Or the global, uh, Bilderberger, conspiracy did it so they can, I don't know, whatever they're doing. Control your mind, steal your underpants, whatever.
And unluckily, the crazy explanation isn't even as unlikely as one would wish. For example, GPS being suddenly "wrong" is a thing that demonstrably happened during the Gulf wars. Aliens? Well no. Bush and Schwarzkopf.
Occam's Razor applies in its mundane (wrongly quoted) form: The simplest solution is always the correct one. Many people go even further, and turn it into: The least disturbing explanation is always the correct one.
So... if something is suddenly definitively weird, then the people observing it either made a mistake, or they're crazy. If there exist too many people worldwide having observed it, and hard, undeniable evidence exists so this solution can be ruled out, then alright, something did happen, but it was a perfectly normal natural phenomenon that we just don't understand yet.
No way has Earth with everybody on it been duplicated by aliens. Because, hey, that is just a crazy, stupid idea. Being external controlled by aliens? Duplicated? Go see a psychiatrist.
Whatever it was, it's most definitively something that happens naturally every few million years, we only just observed it for the first time, and we do not understand it yet. Some, whatever, interference shifting our space-time frame a bit. While we do not have an explanation at hand, we will work out a perfectly normal, non-disturbing explanation related to... black holes, or dark matter, or something.