Will I receive an interference pattern on D0 detector https://en.wikipedia.org/wiki/Delayed-choice_quantum_eraser#The_experiment_of_Kim_et_al._(1999) if D1, D2, D3, D4 exist in the set up of the experiment, but they are thousands of light years far? Simply, to set up the experiment so that I detect all of the signal photons on D0 before I detect any of idler photons!
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1It seems that you are using the notation used in the diagram in this Wikipedia page without mentioning that fact or indeed providing a clear reference to where you get this notation. That is not an appropriate way to write, and you need to edit your post to fix this. – Emilio Pisanty Jul 22 '19 at 18:03
1 Answers
The interference patterns in the delayed-choice quantum eraser experiment are only ever observed via post-selection: using the notation from Wikipedia, the $D_0$ detector will detect a formless blob, which will only resolve into complementary interference patterns once you post-select on detections by $D_1$ and $D_2$ (as opposed to detections by $D_3$ and $D_4$).
As such, the interference patterns can be argued to be "implicit" in the data you've taken, but they can only be revealed once you receive the data from what was measured on the other side. Since you specified that the two sides of the experiments are thousands of light-years apart, this means that you will need to wait for several thousand years after measuring on $D_0$ before you can tease apart the constituent interference patterns in your data.

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Thanks for your answer and your suggestions. To clarify a bit my question: What if D1,D2,D3,D4 do not exist at all? Or, They exist but they are thousand light years apart? I just set up the experiment so that I will receive all of the signal photons on D0, and 1 year after I receive the last signal photon on D0, I receive the first idler photon on any other detector( D1,D2,D3,D4). One second after I receive the last signal photon I start looking at D0 detector! Here I receive signal photons whose "path information" is not known. In that case I should "see" interference pattern on D0! Right? – Vlado Jovanovski Jul 23 '19 at 09:54
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1No. For a detailed answer as to why, see the first paragraph of this answer - it makes no sense to repeat it. – Emilio Pisanty Jul 23 '19 at 12:59
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so what would show up on the detector plate while waiting 1000s of years for the delayed photon to arrive? not sure what u mean by "formless blob". i didnt see that in the wikipedia page – michael Aug 08 '19 at 21:24