 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/ii/paper-2/10d/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Yes. The states

∣ Φ^{+} ⟩

and

∣ Φ^{-} ⟩

are orthogonal, since

⟨ Φ^{+} ∣ Φ^{-} ⟩ = \frac{1}{2} (1 - 1) = 0.

A joint projective measurement in the Bell basis therefore distinguishes them with certainty. Concretely, a controlled-NOT followed by a Hadamard gate converts the Bell basis into the computational basis before measurement.

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