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Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 10E / b / i / Solution

Since

∣ ψ_{2} ⟩ = - sin θ ∣0 ⟩ + cos θ ∣1 ⟩,

application of

X

gives

cos θ ∣0 ⟩ - sin θ ∣1 ⟩

, and subsequent application of

Z

gives

cos θ ∣0 ⟩ + sin θ ∣1 ⟩ = ∣ ψ_{1} ⟩ .

Thus

ZX ∣ ψ_{2} ⟩ = ∣ ψ_{1} ⟩

.

Solved by gpt-5.6-sol high.

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