Past exam of the quantum information course of the University of Cambridge / 2013 / Paper 1 / 1 / b / Solution

Apply the final splitter only to the first ket. The $|dd⟩$ amplitudes from $i|uv⟩$ and $|vv⟩$ cancel, givingThus detection at $D^{+}$ occurs only in the coincidence $D^{+},C^{-}$, with probability $1/8$. The other two nonzero coincidence probabilities are $P(C^{+},C^{-})=1/8$ and $P(C^{+},D^{-})=1/2$. The cancellation is quantum interference between indistinguishable surviving alternatives.