 Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2022/quantum-information/1/b/solution

∣ \pm ⟩ = (∣0 ⟩ \pm ∣1 ⟩) / 2

and

cos θ + i sin θ = e^{i θ}

⟨ \pm ∣ ϕ ⟩ = \frac{2 \pm e ^{i θ}}{6} .

The Born rule gives

Pr (+) = \frac{1}{2} + \frac{2}{3} cos θ, Pr (-) = \frac{1}{2} - \frac{2}{3} cos θ .

The two probabilities sum to one. Their dependence on the relative quantum phase is the quantum interference between the two components in the computational basis.

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