Let us suppose that we have a source that produces a pair of entangled photons in one time instant. One of the photons is sent to apparatus-A and the other to apparatus-B. Apparatus-A and B are experimental set up of double slit experiment. In apparatus-A, it is determined as to which slit the photon passes through and as a result we would not see interference pattern on the screen. However, in apparatus-B no such measurement is done. Would we see an interference pattern on the screen of apparatus-B after sufficiently long time?
If you would have two particles in the singlet state with respect to position and momentum then we know: measuring both particles positions gives equal and opposite outcomes; measuring both particles' momentum gives equal and opposite outcomes; measuring position of one and momentum of the other will give uncorrelated outcomes. This means for the two-slit experiment, with a measurement of "which slit" in one wing of the experiment: both experiments will give the results you would expect for single photons in a completely mixed state, and there is no correlation at the individual level between "which slit" photon 1 takes and "which interference peak" photon 2 ends up in.
When entangled photons are created in Bell-type experiments, it is their polarizations which are entangled. It is not clear to me that their positions or momenta are entangled in the same way. But anyway, engtanglement does not violate "no action at a distance" and in particular there is no way to see at location A what measurement is being made at location B. Therefore it is clear that an interference pattern observed at location B cannot change according to how the photons are measured at location A.
The question is not clear. But I would like to say that entanglement is like a non-local correlation between two bodies. In present case the measurements are independent of each other as told by Prof Gill.
What would happen if we suppose that the position and momenta of the photons are entangled? Would we still see an interference at apparatus B?
If you would have two particles in the singlet state with respect to position and momentum then we know: measuring both particles positions gives equal and opposite outcomes; measuring both particles' momentum gives equal and opposite outcomes; measuring position of one and momentum of the other will give uncorrelated outcomes. This means for the two-slit experiment, with a measurement of "which slit" in one wing of the experiment: both experiments will give the results you would expect for single photons in a completely mixed state, and there is no correlation at the individual level between "which slit" photon 1 takes and "which interference peak" photon 2 ends up in.
See similar questions and answers in the section on quantum erasers in:
http://www.ellerman.org/a-common-fallacy/
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