Alex Torres said:
Then, a definite interference pattern at d0 can be distinguished from an overall pattern at d0 resulting from different outputs being overlapped. Am i correct?
Quick answer: No.
Longer answer:
In one run of the experiment we accumulate a large number of position measurements, basically observations of the form "detector d0 detected a signal photon when it was at position x". We look at these and find a pattern: some areas get more detections than others. It's always the same pattern every time we run the experiment no matter what happens with the idlers, and that's all the information that we ever get from d0. There will never ever be but that one pattern at d0 (unless we change something else like the frequency of the pump laser, or the position and shape of the slits, or the characteristics of the BBO crystal).
Now suppose we take our large collection of position measurements and divide it into four groups. (We could put measurements 1, 5, 9, ... in the first group, 2, 6, 10, ... in the second group, 3, 7, 11, ... in the third group, and 4, 8, 12, ... in the fourth group. Or we could do the assignments randomly: for each measurement we generate a random number between 1 and 4 and put that measurement in that group. Or we could do something else). Then we look at the pattern for each group. Several things should be obvious:
- The total pattern will be the sum of the patterns for each group. It's nonsense to talk about the sum being somehow different from the total pattern (which is why the quick answer above is "no").
- The pattern for any single group doesn't have to look like the total pattern. For example, we could choose to put all the measurements in which x is less than .1 in one group; then we'll find that the pattern for that one group has a huge spike where the pattern for the other three groups has a huge trough, and neither the trough nor the spike appears in the pattern we actually measured. That doesn't mean that we've observed anything different; it's just an artifact of how we've manipulated our data.
There is one particularly interesting way of dividing our collection of position measurements into four groups. We are sitting around admiring the nice pattern we found at d0 when Alice walks up to us and suggests that we try putting this one, this one and this one into group one, then that one and that one into group two, and so forth. We're intrigued, so we ask her how she's choosing, and she explains that she's putting all the ones whose idler triggered d1 into one group, all the ones whose idler triggered d2 into another group, and so on. So we divide our collection of position measurements into four groups as Alice suggests, then we look at the pattern for each group in isolation... and we get something that looks like the patterns in Kim's paper, with interference fringes in groups 3 and 4 and not in groups 1 and 2.