 Solution

ID: past-exam-of-the-laser-science-and-quantum-information-processing-course-of-the-university-of-oxford/2021/6/d/solution

Suppose the conditional atomic pure state were a product state

(α ∣ e ⟩ + β ∣ g ⟩) \otimes (γ ∣ e ⟩ + δ ∣ g ⟩) .

Comparing its four probability amplitudes with

(∣ e g ⟩ + ∣ g e ⟩) / 2

gives

α γ = 0, β δ = 0, α δ = \frac{1}{2}, β γ = \frac{1}{2} .

The last two equations make all four factors nonzero, contradicting either of the first two. Equivalently, the coefficient matrix has determinant

- 1/2

I /2

, making the conditional state maximally entangled.

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