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Its a question about entangled pairs and double slit experiment. I have seen and read many such on the stackexchange but I can not really understand what is happening! So please don't stop the question as a duplicate.

I would like to get an answer about an extremely simple scheme which is close to that of Birgit Dopfer one 1999.

  1. One has a pairs of path-impulse connected photons.

  2. Photons A are headed on to a double slit DS and later on to a CCD (A) to register the pattern.

  3. Photons B are headed on to another CCD (B) and are registered just exactly when photons A passed the DS (or pass).

  4. What I expect is that because the positions of photons B would be well known hence so are the positions of photons A and one knows which way the photons went through the DS. This makes the interference pattern disappear. In this case CCD (A) doesn't show interference picture.

  5. Then one switches CCD B off. Now there is no which way information anymore. So there must emerge an interference pattern.

And most importantly its not necessary to use a coincidence circuit for the photons A and B (as it is in Dopfer experiment). The flux of photons A now is just a common flux of photons which are no more entangled so it would give simply an interference pattern. If this is not the case I would like to understand which of the basic rules of QM prevents it?

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    $\begingroup$ just a general comment/advise: not many people are going to be willing to read through a wall of text such as this one. Proper formatting of questions is very useful to improve your chances of getting good answers. $\endgroup$ – glS May 20 at 0:07
  • $\begingroup$ @glS thank you. I realized that one must include two enters in his text in order to get one here. $\endgroup$ – Mercury May 20 at 5:14
  • $\begingroup$ "path-impulse connected photons"? $\endgroup$ – probably_someone May 20 at 6:01
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Entanglement doesn't mean that measuring one photon gives you all possible information about the other photon. Entanglement connects certain specific pieces of information about the two photons, and those pieces of information have to be derived from properties that are accessible when making the entangled system.

For example, you can create two photons that have entangled polarizations. You can, for instance, entangle them such that the polarizations are always measured to be the same. Suppose your entanglement process doesn't result in the photons' directions being correlated. In that case, measuring the polarization of one photon would tell you the polarization of the other photon, but measuring the direction of one photon would tell you nothing about the direction of the other photon.

If you want this setup to work, you have to entangle the photons at the beginning in such a way that some property of photon B is entangled with the "which-path" information of photon A. You also have to measure this property at CCD B. If this isn't the case, then measuring photon B won't tell you anything about photon A and won't affect the interference pattern. On the other hand, if this is the case, then this seems like a valid version of the quantum eraser experiment.

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  • $\begingroup$ probably_someone @probably_someone Are you implying that there are no direction-impulse entangled sources? Look at the paper of Zeillinger 'Experiment and the foundations of quantum physics'. Here the point is why Dopfer uses coincidence counts to get the interference pattern. Cramer 'An Inquiry into the Possibility of Nonlocal Quantum Communication' has reviewed Dopfer work and also wondered why was the coincidence needed. $\endgroup$ – Mercury May 26 at 18:38
  • $\begingroup$ He attributes it to technical problems: 'From the point of view of moving to a path-entanglement situation in which the coincidence requirement could be relaxed, the problem with both of the experiments discussed above is that their use of a two-slit system blocks and absorbs most of the photons from the nonlinear crystal that illuminate the slit system. Further, the down-conversion process is intrinsically very inefficient (∼1 photon pair per 108 pump photons).' But this can not be the reason. There must be a very deep reason. $\endgroup$ – Mercury May 26 at 18:51
  • $\begingroup$ Maybe the no-deleting theorem has an issue here? $\endgroup$ – Mercury May 27 at 6:29

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