 Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2022/quantum-information/3/c/i/solution

The state is separable. The identity matrix resolves into the four projectors of the computational basis, giving the explicit quantum state ensemble

\frac{I _{4}}{4} = \frac{1}{4} i, j = 0 \sum 1 (∣ i ⟩ ⟨ i ∣)_{A} \otimes (∣ j ⟩ ⟨ j ∣)_{B} = \frac{I _{2}}{2} \otimes \frac{I _{2}}{2} .

Each member is a pure state that is a product state, so this is a separable quantum state by its defining decomposition.

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