Please take a look at this experiment https://en.wikipedia.org/wiki/Delayed-choice_quantum_eraser#The_experiment_of_Kim_et_al._(1999) . You can also look at this youtube video https://www.youtube.com/watch?v=H6HLjpj4Nt4 describing the same experiment.

What would be the result of the experiment above at D1, D2, D3 and D4, if I put a detector at both slits so that the "which way" information is detected immediately at the slits?

See the picture below for clarification:

enter image description here

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    $\begingroup$ Hello, it would help if you could give some more context as to what is happening in the image... what are the elements, what's happening, or could you point us to a similar setup somewhere else? Also could you be more precise as to what specifically you mean by the "result of the experiment @ D1, D2, D3, D4", what is the observable? $\endgroup$ – Gyromagnetic Jul 1 '19 at 20:31
  • $\begingroup$ Think of light as a wave function that can see everywhere, chooses the best path, some probability involved, and voila the energy is transferred between 2 atoms (electrons). If one starts to change the paths available to the "photon" or "wave function" it adjusts accordingly and still picks an ideal path. Also I do not believe the BBO/prism is a detector, it is more of a deflector, any photons created in pairs become part of one wave function. $\endgroup$ – PhysicsDave Jul 2 '19 at 1:33
  • $\begingroup$ It's impossible to get which way with a detector without destroying the photon. $\endgroup$ – PhysicsDave Jul 2 '19 at 1:35
  • $\begingroup$ @PhysicsDave If by "destroying" you mean "absorbing" then your comment is wrong; perhaps you should clarify your comment. $\endgroup$ – Andrew Steane Jul 4 '19 at 12:31
  • $\begingroup$ Don't be too drawn in by concepts such as "delayed choice" and "quantum eraser"; they are just names for aspects of ordinary quantum mechanics. It was appropriate to discuss them at length 50 years ago, but experiments of this type no longer have anything to teach us about quantum physics. In this sense they are not so much research as the sort of demonstration one might employ in a lecture in order to illustrate an established idea. $\endgroup$ – Andrew Steane Jul 4 '19 at 12:37

The whole purpose of the setup is to erase the path information of electron. If a detector is put at the slits, it would mean we have the path information and the electrons would behave like matter particles. I would say watch the first 2 minutes of the video link that you shared. It would not matter if later the path information is erased because we already have the info to begin with( which wasn't the case in the original experiment). The possession of the knowledge collapses the wave-function which we obtain as soon as we place a detctor at the slits and the wave form collapses there it self.

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