 Solution

ID: past-exam-of-the-quantum-information-course-of-the-university-of-cambridge/2013/paper-1/1/c/solution

Interchanging the two wings gives

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

Now detection at

D^{-}

occurs only together with

C^{+}

1/8

. The remaining nonzero coincidence probabilities are

P (C^{+}, C^{-}) = 1/8

and

P (D^{+}, C^{-}) = 1/2

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