I wanted to re-open the question of quantum measurements across event horizons. If I set up two slits or more generally a diffraction grating which crosses a black hole event horizon, and I shoot a stream of appropriate particles at the slits/grating, will I observe an interference pattern on a detector placed on the far side of the slit/grating and also crossing the event horizon?

It seems to me that the previous discussion was focused on the perspective of the observer or observers within or without the horizon, not the particles themselves. A double slit experiment does not involve EPR-like entanglements of multiple particles, if I understand correctly it works through the adding up of detections of "individual photons" (whatever that means; otherwise we can posit electrons or buckyballs which certainly seem to have some kind of particulate behavior at least sometimes). Very naively, if a photon or other particle is fired at a screen with a double slit, in which one slit is just outside and the other just inside the event horizon, it seems to me that there is still a potential problem regarding whether interference will occur. The wave function itself is not a mass-energy construct, hence does not obviously respond to the structure of spacetime. Given that the nonlocal aspects of QM leading to interference fringes are a problem even in flat spacetime, I don't see how they become any less difficult in curved spacetime.

Is there a trivial objection to proposing that interference fringes would build up with multiple particles, just as in any double slit experiment, indicating that QM waves, whatever those are as well, are immune to event horizons? Clearly only that part of the detector screen lying outside the horizon would be accessible to the observer. Note that spin is not an issue in this experimental design, so some of the papers I have read which deal with the interaction between particles with spin with black holes (especially rotating ones) would not seem to be relevant in this design.