 Solution

ID: past-exam-of-the-laser-science-and-quantum-information-processing-course-of-the-university-of-oxford/2021/3/b/ii/solution

ℏ V σ_{x} /2

. Therefore

U (τ) = e^{- iV τ σ_{x} /2} = R_{x} (V τ), δ = 0, τ = \frac{π}{2 V} .

It gives the requested positive rotation about the x-axis. In the ordered basis

(∣1 ⟩, ∣0 ⟩)

∣1 ⟩

becomes

(∣1 ⟩ - i ∣0 ⟩) / 2

(0, - 1, 0)

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