 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-1/10e/a/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

A final oracle call evaluates

f

on the definite input

a

∣ Φ_{3} ⟩ = (- 1)^{b} ∣ a ⟩ ∣1 \oplus f (a)⟩ = (- 1)^{b} ∣ a ⟩ ∣1 \oplus a \cdot a \oplus b ⟩ .

Since

a \cdot a

a

, this form also determines the last-qubit measurement.

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