Understanding the Delayed Choice Quantum Eraser Experiment

[Cobalt101]

I've been reading Brian Greene's "The Fabric of the Cosmos" and am currently at the description of the delayed choice quantum eraser experiment. My understanding is that this can be set up so that the idler photons can be measured (long) after the signal photons hit the detector screen. Under such an arrangement when the signal photon detector screen is examined, there will be evidence of whether there is an interference pattern or not. If subsequently the idler detection is examined and beam splitters a and b are operating, then the signal photon screen will have shown an interference pattern just for the subset of signal photons for which their associated idler photon went via the beam splitters. If the beam splitters were not operating, then no interference pattern would have been observed. I am thinking that if the experiment is set up so that a delayed choice can also be deployed such that all idler photons go through "the maze" and into detectors 2 and 3 then a full interference pattern would have been observed for the signal photons. At the time of the signal photon detection all that can be seen is an interference pattern (indicating individual photons traveled via both paths) or no interference pattern (indicating that individual photons have traveled using only one path, but we would not have the information as to which path at that time). But if all of these options re the treatment/path/detection of the idler photons can we decided well after the signal photon detection has occurred, what if the option selected for the idler photon is inconsistent with the signal photon outcome (interference pattern or no interference pattern) ?

 

[Strilanc]

The short answer is that Brian Greene didn't do a great job of explaining the setup, and you've misunderstood what actually happens.

Here's a diagram I keep using again and again:

Notice that, regardless of what the choice will be, you initially see no interference pattern. To find an interference pattern you have to go in after the fact and group the individual screen measurement outcomes based on the associated measurement result you got from the chose-to-erase process.

Also, you can understand the experiment by thinking in terms of the screen's measurement result telling you information about how the 'eraser' L+R vs L-R measurement will be biased. Everything is happening forward in time.