The prediction for what happens when you block the B to D path is wrong. We have three final configurations, not two as in the above.

* From the configuration "A photon going from B to D", with original amplitude (1 + 0i) o Amplitude of (1 + 0i) * 1 = (1 + 0i) flows to "Block with absorbed photon". * From the configuration "A photon going from C to D", with original amplitude (0 + -i) o Amplitude of (0 + -i) * i = (1 + 0i) flows to "A photon going from D to F" o Amplitude of (0 + -i) * 1 = (0 + -i) flows to "A photon going from D to E".

Applying the magical detector, we get a 1/3 probability for each of these outcomes; detector 1 detects, detector 2 detects, neither detects (block absorbs photon).

Does this work?