There's already two good answers that say a lot of what I wanted to say, and I will refrain from repeating any of their content here. I do think it is useful to add one more item of insight though. You say:
"any quantum switch in this universe can be flipped instantaneously from
elsewhere."
When people talk about a "quantum switch flipping instantaneously", they are referring to entangled states of the form:
$$
N\left(|01\rangle + |10\rangle\right),\tag{1}
$$
which simply means that that if you measure this system,
- there is a 50% chance of the measurement telling you that qubit 1 is in state 0 and qubit 2 is in state 1 (the first state in the equation), and
- there is a 50% chance of the measurement telling you that qubit 1 is in state 1 and qubit 2 is in state 0 (the second state in the equation).
By making the measurement on qubit 1 and getting a 0 or 1, qubit 2 is instantaneously going to become a 1 or 0 (the opposite of the qubit 1), but:
- We do not know what the other state is without going there and measuring it, because we do not know that the original state is $N(|01\rangle + |10\rangle)$. If we measure qubit 1 and get 0, the original state could also have been $N(|00\rangle + |11\rangle)$ meaning that the other state instantaneously becomes a 0, not a 1. You would either have to spend time traveling to qubit 2 and measure it to find out if the original state was more like $N(|00\rangle + |11\rangle)$ or more like $N(|01\rangle + |10\rangle)$, or you could have someone located near qubit 2 and measuring it at the same time as you measure qubit 1, but then they would have to send a signal to you about the result they measured and it will time time for this signal to reach you. So no information has traveled instantaneously.
- Nothing is really being "flipped" or "switched". To be flipped or switched implies that something was a 0 and became a 1, or was a 1 and become a 0, but none of that is happening here. We have a qubit that is neither in state 0 nor 1 (it is in a superposition of 0 and 1), and it becomes a 1 or 0 depending on what the other qubit becomes after the measurement.
- The entire principle does not just apply for any quantum state, it only works for entangled states. If the state was $|00\rangle$, then qubit 1 and qubit 2 are both going to be 0 no matter what, and the measurement outcome for qubit 2 does not depend at all on the measurement outcome of qubit 1.
So these are the points to remember:
- The state of qubit 2 changing depending on the measurement of qubit 1, does not apply to any state but only entangled states.
- Nothing is being "switched" or "flipped" like a light switch flipping from off (0) to on (1). A state goes from being in a superposition of 0 and 1, to being in only one of 0 or 1.
- There is no illusion that information is traveling faster than the speed of light to anybody other than maybe qubit 2 itself. You can think of qubit 2 receiving the signal from qubit 1, that qubit 1 was found in state 0, which leads to qubit 2 settling instantaneously in state 1, but that signalling happens within a single entangled system. Nothing outside of that entangled system is able to witness any super-luminal information transfer. To know that information traveled from qubit 1 to qubit 2 you or someone else would have to measure qubit 2 and the information about the measurement outcome would have to travel from the measurement device to you, which will take time.
Regarding the last point: What if the measurement device measures the states of qubit 1 and qubit 2 at the same time? Does the measuring device witness super-luminal information travel? Well no, because how does the measuring device know that the original state was even entangled? It could have been originally in the state $|01\rangle$ meaning that qubit 1 was in state 0 and qubit 2 was in state 1 the entire time, and no "instantaneous change" occurred.
What about if qubit 2 is a measuring device? The measuring device settles on state 1 immediately when qubit 1 is found to be in state 0, so has the measuring device witnessed super-luminal information travel about the state of qubit 1? Again, this would only be true if the measuring device (qubit 2) knew that it was entangled with qubit 1, and you cannot "know" what state something is in without first measuring it, but measuring this state would mean collapsing its wavefunction into a non-entangled state. So you cannot "know" this state was entangled without making it non-entangled, and if it's non-entangled there is no "instantaneous" information transmission. The measuring device therefore sees the effect of the "instantanous" information transmission but is unable to know whether any information was transmitted at all or if the states were just like that all along. This problem would be the same if the measuring device was both qubits 1 and 2 (the device finds out the states of both qubits at the same time, but it doesn't know whether or not information was transmitted because it cannot know whether or not the qubits were previously entangled, without having un-entangled them).
Then the final question becomes whether or not qubit 2 really changed instantaneously based on the measurement outcome of qubit 1. The theory of how quantum states and measurements work tells us that if the qubits are in the state described by Eq. 1 and qubit 1 is measured to be 0, qubit 2 "instantaneously" settles in state 1, but is there a way to experimentally verify this theory that qubit 2 "instantaneously" settled on state 1? Assume that it takes time, maybe the distance between qubits 1 and 2 divided by the speed of light, for qubit 2 to settle on state 1, then maybe you can come up with some experiment where you do multiple successive measurements and the results would contradict the hypothesis of there being a "delay" in qubit 2 settling on a state? Perhaps that could be the case, but consider for a moment that there is not really any "distance" between qubits 1 and 2, since they are really just one entangled system. If there is zero distance between them, then the speed of information travel does not have to be faster than the speed of light in order for the information to travel 0 metres, so the question now becomes whether or not you can prove that qubits 1 and 2 were more than 0 metres apart at the time of being entangled, and whether or not you can do this without doing any measurements (since measurements un-entangle the qubits) and fast enough to know that the qubits didn't move before your measurement finished.
