 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2005/iii/paper-37/2/b/ii/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

∣Ψ ⟩ = (\frac{∣0 ⟩ - ∣1 ⟩}{2})_{A} \otimes (\frac{∣0 ⟩ - ∣1 ⟩}{2})_{B} .

This is already a Schmidt decomposition with one term. Consequently

r = 1, s_{1} = 1, λ_{1} = 1.

(∣0 ⟩ - ∣1 ⟩) / 2

, so its other eigenvalue is zero. The joint pure state is a product state, with no entanglement.

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