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I've recently watched PBS SpaceTime's video about the quantum eraser. In it, Matt describes a kind of crystal that splits particles into pairs and entangles them. The entangled particles are then delivered into the quantum eraser part of things. My question is, if we remove all the detectors and half-silvered mirrors and whatnot and let the other entangled particle fly off into space, undisturbed and undetected, would an interference pattern still emerge since we would not obtain the path information?

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No, an interference pattern will not appear.

The key criterion whenever which-way information is involved is whether the information is available in principle, regardless of whether we detect it or not. The presence of the half-silvered mirrors and the detectors A and B (in PBS Space Time's notation) is irrelevant: the photon flying away is entangled with the photon that hit the screen, and in that entanglement it carries the which-way information of what slit both went through.

The only way to restore the interference pattern is to completely erase the which-way information, in a way that makes the reconstruction of which slit the photons went through impossible even in principle. The standard way of doing it is the one explained in the video (i.e. by making a coherent measurement between the two options, and then post-selecting out on the both outcomes, which will separate out the two overlapping complementary interference patterns on the screen), but in general the procedure needs to be coherent, it needs to perform a nontrivial projective measurement on the existing which-way information, and it needs to do a correlated post-selection to get anything meaningful.

If you don't do any of that (say, if you just let the which-way information fly away) then the interference pattern won't come back.

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  • $\begingroup$ So, the photons hitting the screen will act like particles while their which-way information is in principle obtainable. So, in the original experiment, one entangled photon is set to hit the screen and another is set to interact with the eraser after the first had already hit the screen. In that brief time between the first photon hitting the screen and the second hitting the eraser, is an interference pattern not present? (Because the which-way information is still at large and in principle obtainable.) $\endgroup$
    – BMF
    Commented May 13, 2019 at 23:49
  • $\begingroup$ Interference patterns are never present unless you post-select out the hits in correlation with the quantum eraser measurements. $\endgroup$ Commented May 14, 2019 at 8:37
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There is quite some confusion about this experiment, which is fed by some simplified explanations on youtube. The experiment can be quite easily understood if you let go of the idea that a photon behaves as a particle. A photon behaves as a wave package, consisting of a quantizised wave or superposition of waves. This is what QM tells us. Then 'which-way' is no valid property any longer; the photon always moves through both slits. It is only reduced to a single location at the point of measurement. See my video for detailed explanation of the experiment: https://m.youtube.com/watch?v=e-uopGrghFQ

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