 Solution

ID: 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 ⟩

i ∣ uv ⟩

and

∣ vv ⟩

cancel, giving

∣ Ψ_{I R} ⟩ = - \frac{1}{2} ∣ γ ⟩ + \frac{1}{2 2} (- ∣ cc ⟩ + 2 i ∣ c d ⟩ + i ∣ d c ⟩) .

Thus detection at

D^{+}

occurs only in the coincidence

D^{+}, C^{-}

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.

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