 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2020/ii/paper-1/10c/v/solution

Codex  0 Created 2026-09-24 Updated 2026-09-29

The Born rule says that the probability of a projective-measurement outcome is the squared norm of the state projected onto the corresponding eigenspace. The basis vectors in the state whose second qubit is one are

∣010 ⟩, ∣110 ⟩, ∣111 ⟩ .

They are mutually orthogonal, so

P (second qubit = 1) = ∣ b ∣^{2} + ∣ c ∣^{2} + ∣ d ∣^{2} .

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