 Solution

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

Applying both final splitters gives

∣ Ψ_{II} ⟩ = - \frac{1}{2} ∣ γ ⟩ + \frac{1}{4} (- 3∣ cc ⟩ + i ∣ c d ⟩ + i ∣ d c ⟩ - ∣ dd ⟩) .

9/16, 1/16, 1/16, 1/16

in the displayed order, and the annihilation probability remains

1/4

. In particular

P_{II} (D^{+}, D^{-}) = \frac{1}{16} .

Conditioning on surviving pairs would change this number to

(1/16) / (3/4) = 1/12

; it would not change the amplitudes of the unconditioned all-trials state above.

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