Simplified delayed choice quantum erazer experiment: is it possible to create an interference pattern at D0?

If we were to create a much simpler experiment by replacing all detectors and equipment by two screens S0 and S2, would it be possible to visually see an interference pattern if we tried (pick a suitable distance and angle for the screens S0 and S1, make sure we pick the right beams coming off the SPDC)?

I know that SPDC are rare events, so most photons would be noise on the screen. Let's assume for a moment that we had a more efficient SPDC.

If the answer is no: why not? (Assuming noise is not the issue). Do we need any additional equipment (which kind)? I understand that the photons that come off the SPDC are not the same as the original photons produced by the laser. So if no interference pattern is possible because of the SPDC, then I don't understand why we would be able to get an interference pattern then in the full experiment as described on the Wikipedia page when adding BSc, D1 and D2?

In case the SPDC is the issue, then how about replacing it with beam splitters? Would we see an interference pattern in that case?

For reference, here is the full set up:

• I was similarly confused the other day and I came across this answer which seems to indicate that you would not get an interference pattern: physics.stackexchange.com/questions/350945/…. I still don't fully understand it though, so hopefully someone can provide another explanation. Feb 7, 2021 at 22:46
• This question definitely needs a better answer. I hope someone may explain why there is no interference pattern in the simplified setup with more detailed clarification. Also why and what logic govern the filtering out of the interference pattern? May 24 at 17:10

You would not get an interference pattern. The no-signaling theorem, together with a similar theorem about unitary operators, says that no matter what you do to just the idler photons, they can't affect the signal photons in anyway. As you know, in the full setup, you don't get interference when you look at $$D_0$$ in isolation. So, even if you replace the full setup with your simplified setup, the pattern on $$D_0$$ won't change.