 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-324/3/a/i/solution

Codex  0 Created 2026-10-03 Updated 2026-10-05

∥ A ∥ = sup_{v \neq = 0} \frac{∥ A v ∥ _{2}}{∥ v ∥ _{2}} = λ_{m a x} (A^{†} A) .

X_{1}

and

Z_{2}

act on different qubits, and each is a unitary operator. Their product is therefore unitary and preserves the norm of every vector. Hence

∥ X_{1} Z_{2} ∥ = 1.

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