Quantum eraser experiment is explained in this youtube video in a basic way.
Correct me if I am wrong but I understand it like this:
Detectors A and B are placed further from the splitting crystal than the interference screen. C and D in the eraser part are placed even further. So:
If detectors A and B are active, then we will not see an interference pattern on the screen even if the idler photon has not reached to A or B yet.
If we deactivate detectors A and B, then just by looking at C and D, we will not be able to deduce which slit the photon went through; therefore, we will observe an interference pattern on the screen.
Now, there are some limitations in the experiment like the conversion rate of the entanglement-crystal. Only a very small amount of incoming photons are converted into two entangled photons. Therefore we must use a coincidence circuit to distinguish them from the non-entangled majority. This implies that it is not possible to detect the interference pattern instantly. We must collect data over time and take the superposition of the relevant photons with the help of the coincidence circuit.
But, is it theoretically possible to affect the interference pattern instantly by activating /deactivating the eraser detectors? Assuming the efficiency of the entanglement-crystal is 100% and the eraser detectors are positioned 1 light-year away from the interference screen, does the interference pattern on the screen change at the same instant that we switch the detectors on /off? Do you know anything on this?
P.S. I edited the question considerably. @benrg's answer was for the previous version.