 Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2021/quantum-information/3/a/ii/solution

\frac{∣ ++ ⟩ + ∣ -- ⟩}{2} = \frac{∣00 ⟩ + ∣11 ⟩}{2} = ∣ Φ^{+} ⟩ .

Prepare $∣00 ⟩$ , apply $H$ to the first qubit, then apply CNOT from the first to the second. The intermediate state is

(∣00 ⟩ + ∣10 ⟩) / 2

, and the controlled-NOT gate gives the required Bell state. No final basis change is needed: the two displayed expressions represent exactly the same vector.

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