 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-2/10d/b/i/solution

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

The controlled-NOT leaves computational-basis signals unentangled:

∣0 ⟩_{A} ∣0 ⟩_{E} \mapsto ∣00 ⟩, ∣1 ⟩_{A} ∣0 ⟩_{E} \mapsto ∣11 ⟩ .

For the two Hadamard-basis choices it gives

∣ + ⟩_{A} ∣0 ⟩_{E} \mapsto \frac{∣00 ⟩ + ∣11 ⟩}{2} = ∣ ϕ^{+} ⟩,

∣ - ⟩_{A} ∣0 ⟩_{E} \mapsto \frac{∣00 ⟩ - ∣11 ⟩}{2} = ∣ ϕ^{-} ⟩ .

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