It is said that if two particles are entangled that if one collapses, the other one collapses as well. Therefore it seemed reasonable to me that in those scenarios different probability wave functions will be measured:
In the first scenario, the photons collapse before the slit.
Two photons are entangled, one is sent to Path A, one to Path B
The photon at path B is measured
The photon at path A collapses
That photon goes through the slit
No interference pattern is observed on the screen
In the second scenario, the photons collapse near the screen.
Two photons are entangled, one is sent to Path A, one to Path B
The photon at path A goes through a slit
The photon at path B is measured when the photon at path A is close to the screen
The photon at path A collapses when it is close to the screen
An interference pattern is observed on the screen
So when the particle collapses before the slit there will be no interference pattern. And when the particle collapses close to the screen, there will be interference. Quite straightforward, isn't it?
But actually, this is not how it works.
What is wrong here with the reasoning?
When an entangled pair of photons is used there will never be an interference pattern. So the first scenario can not exist. Whatever you do with the entangled photon, the pattern produced by the photon heading to the detector will always be the same.
In fact, it would have been quite weird if those scenarios worked according to the figures. Because that would mean that messages could easily be transmitted by entangled photons just by deciding to measure or not to measure. That would result in faster-than-light communication and that is, as far as we know, not how physics works :)