 Solution

ID: past-exam-of-the-short-options-paper-of-the-physics-prelims-of-the-university-of-oxford/2022/s03/2/e/solution

x +

∣ ⟨ x + ∣ ↑ ⟩ ∣^{2} = 1/2

. The selected quantum state

∣ x + ⟩

then yields

z -

with conditional probability

∣ ⟨ ↓ ∣ x + ⟩ ∣^{2} = 1/2

. Relative to the original beam,

p (x + then z -) = \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4} .

Among particles reaching the second apparatus, the negative-

z

1/2

; the requested fraction uses the original intensity and is

1/4

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