Based on my understanding of the “Double-Slit Quantum Eraser Experiment”, documented here: http://grad.physics.sunysb.edu/~amarch/, it seems that Faster-Than-Light communication is possible. Of course, this violates the “no-communication theorem”, so I assume it’s due to a misunderstanding on my part.
In the experiment, changing whether the polarization of the ‘p’ photon is erased or not changes whether or not interference patterns appear for the ‘s’ photon. Suppose Alice and Bob generate many entangled photons and then travel to opposite sides of the galaxy, Alice taking the ‘p’ photons and Bob taking the ‘s’ photons. At a predetermined time Bob releases his photons one by one into a double slit setup as in the experiment. If he sees an interference pattern, he knows that Alice must have “erased” the polarization information on her corresponding ‘p’ photons, and if not that she has instead measured it.
Of course, even stranger situations are possible. The fact that the ‘s’ photon in the experiment showed interference patterns when the ‘p’ photon was going to be erased, but hadn’t been yet, makes me think that photons can retrieve information from the future. For instance, measuring the ‘s’ photon and detecting interference patterns or not, while the ‘p’ photon is bouncing around in some system, waiting to have its polarization be either erased or measured depending on the result of some future event, like an election result. If the ‘s’ photon shows an interference pattern, then you would know the result of the electron (or know that forces beyond your control erase the information for some other reason).
I’d be very appreciative if you could clear this up for me. My search online has not been fruitful, since the only similar questions I’ve seen just say something like “When you have entangled photons, measurements on one member of the pair cannot tell you anything about whether the other member has been measured or not.”, which seems to be contradicted by the above experiment.