I found the calculation of the amplitude flows for cases 1 to 4 confusing at first. I think the part I missed is that the reflection of a photon at a half silvered mirror multiplies the configuration (ie the state of both photons) by i. So in case 1 we get each photon multiplied by i twice, so the amplitude at both detectors is 1.
I found the calculation of the amplitude flows for cases 1 to 4 confusing at first. I think the part I missed is that the reflection of a photon at a half silvered mirror multiplies the configuration (ie the state of both photons) by i. So in case 1 we get each photon multiplied by i twice, so the amplitude at both detectors is 1.