Double-slit quantum eraser: measured patterns on screen

[msumm21]

Consider a double-slit quantum eraser experiment such as the one by Walborn et al (http://arxiv.org/abs/quant-ph/0106078). The overall pattern formed by the signal photons on the screen behind the double slits is the same regardless of whether which-path information is available or destroyed (plot of "N Vs X" looks something like a scaled up Gaussian). In the case that the which-path information is destroyed, the verified explanation is that the net pattern is the sum of two offset interference patterns (one when the idler collapsed to $|+\rangle$ polarization in the Walborn case, and one for $|-\rangle$). In the case the which path information is accessible, no such interference patterns occur and as far as I know it is a coincidence that the math works out such that the net pattern is the same.

Is it really just a coincidence that these patterns are the same? I'm assuming there is an explanation of these experiments which makes this result fall out automatically (something better than just "it has to be that way to preserve causality"), right?

 

[msumm21]

I'm struggling to accept this as a mere coincidence. The total net pattern that appears on the screen is always the same, call it P. In one series of experiments the polarizer POL1 is absent and hence which-path information is available giving two patterns G1 (for the photons that pass through slit1) and G2 (for slit2). P = (G1+G2)/2. This at first seems fine. Then the experiment is repeated passing the idlers though a polarizer POL1 and the idlers passing through POL1 (at the fast axis of QWP1) correspond to signalers that make an interference pattern called "I1." Similarly, those that pass through POL1 at the fast axis of QWP2 make a different interference pattern "I2." But now the fact that G1+G2=I1+I2 seems amazing to me because I don't see any physics here that should enforce that. I realize that, if it's not true then causality would seemingly fail, but I don't know what the mechanism is here for enforcing this. Anyone else puzzled by this? Anyone find a way to accept it?