DTQE idler photons fall into a Black Hole- interference at d0?

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bcrelling
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Experiment:

Imagine the dalayed time quantum eraser experiment, except the pair of "idler" photons(which would normally pass onto the detectors d1,d2,d3,d4) instead fall into a black hole.

Would d0 detect interference or not?


It seems commonly accepted that the information of in-falling matter is preserved when the black hole evaporates through Hawking radiation. However before the evaporation we don't have access to the information. Does this mean that we observe interference(due to absence of which-path information) yet when the Hawking radiation comes out of the BH the past is retroactively altered to one where interference wasn't observed?!
 
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It is not clear whether d0 would detect interference or not in this experiment. There are various theories about how information is preserved in a black hole, but until further research is done it is impossible to say what the outcome of this experiment would be.