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Here's the delayed choice quantum eraser setup from Kim et al. (1999), from Wikipedia. Don't worry, we're going to throw out almost all of it.

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An argon laser generates individual 351.1 nm photons that pass through a double-slit apparatus (vertical black line in the upper left corner of the diagram). We color code the two paths, but of course all photons and paths are the same color (wavelength). After the slits, spontaneous parametric down-conversion (SPDC) creates an entangled two-photon state.

The 702.2 nm photon that moves toward the upper right is referred to as the "signal" photon, the other the "idler" photon. I'm modifying the setup so that the idler photon goes through an equivalent setup as the signal photon:

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My question is: do we see an interference pattern at both detectors $D_0$ and $D_*$? Or no interference pattern?

If there's no interference pattern: where is the which-way information? Either branch is basically a traditional two-split experiment, so I don't understand why there would be which-way information here, when there's none in the traditional. Where did it come from? Where is it living? How does it escape the setup into the macroscopic world?

If there is an interference pattern at both: then extend the length of the bottom path. This shouldn't change interference/no interference pattern. Now, after we get a detection at $D_0$, which we agree should follow the interference pattern in aggregate, swap out $D_*$ for a different setup that detects the two beams independently, thus measuring the which-way information.

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There are a few other things going on: 1) in Kim they used a coincidence circuit to separate the signals D1,D2,with D3,D4 and 2) for some reason there is a "phase difference" where the detected patterns were actually of complementary shape .... let's keep that in mind.

In your setup the coincidence detector is necessary to observe the complementary patterns .... and yes the patterns are forming! (otherwise you will just see the lump).

If you add the 2 new path detectors there's no interference detected ... your setup has forced the EM field NOT to interact with the slits ... the paths are emitter ... single slit ... detector. There are also many more photons emitted by the crystal, much more that the ones in the narrow pathways pathways leading to the detectors ... those photos are free to make the pattern.

The EM field (initiated by an excited electron) interacts with the whole apparatus before emission even occurs .... emitter, slit(s) (single or double) crystal, prism, detector (free to see both slits) or detector (locked into one slit).

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