If I know in advance I'm getting an interference pattern, wouldn't I have time to remove the splitter so the which-path information would be know?

Question

Check the image below, from this excellent explanation of the quantum delayed eraser. My question, and please forgive me if it is a naive one, is that first the photon reaches detector A, which tells us whether we have an interference pattern or not. With this information in hand, and because the second detection to know the which-path information is delayed for minutes or even millions of years, won't we have enough time to just remove the splitters and always send the entangled particle to detectors 2 and 3, effectively revealing the which-path information and causing a contradiction?

My point is that if I first look to find an interference pattern on detector A and then wait for a couple of millions years so I have time to effectively remove the splitters before going back to look again at detector A, will I find that my first observation has mysterious changed to the double line pattern, in other words, the future has just changed the past because what I first saw with my own eyes was an interference pattern that has now turned to a double line pattern?

Has anyone tried this experiment?

Answer 1

The video doesn't give an explanation of the delayed choice quantum eraser - that is, an account of what is happening in reality to produce the results of the experiment. The video states the results of the experiment unclearly. The original paper

https://arxiv.org/abs/quant-ph/9903047

or even the wikipedia entry on this experiment:

https://en.wikipedia.org/wiki/Delayed-choice_quantum_eraser

are less misleading.

When the photon is measured at detector 1 all you see is a blob. If you only looked at the results from that detector you would never know what happened to the other photon. If you compare the results from detector 1 to those from detector 4 then you see that the probability of a photon arriving at the same position varies in an interference pattern with position. If the photon arrives at detectors 2 and 3 then you don't get that pattern in the comparison, but the pattern detected by measuring the results of detector 1 alone are just a blob. So if you remove the splitters and the photons arrive only at detectors 2 and 3 there will be no way to know that by looking at the results of measurements at detector 1 alone since the interference pattern or lack thereof is a pattern you get when you compare the results of measurements at detector 1 to detectors 2,3 and 4.

I think the explanation for these results is that all of the possible outcomes happen and the correlations are established when the measurement results are compared:

https://arxiv.org/abs/quant-ph/9906007

https://arxiv.org/abs/1109.6223

The more standard account is that somehow what happens at one detector affects what happens at the other. But even in that account, there is no prospect of knowing whether there is a beamsplitter at detectors 2,3 and 4 if the results of this process somehow agree with quantum mechanics.