 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-3/15e/b/solution

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

Conjugating a reflection by a unitary reflects in the transported vector. Since

A ∣ 0^{n} ⟩ = ∣Ω ⟩

A R_{0} A^{- 1} ∣Ω ⟩ = - ∣Ω ⟩,

and every vector orthogonal to

∣Ω ⟩

is fixed. Hence

A R_{0} A^{- 1} = R_{∣Ω ⟩},

in particular both sides act identically on

∣Ω ⟩

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