 Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2023/quantum-information/1/a/ii/solution

{∣ b_{j} ⟩}_{j = 0}^{d - 1}

ρ

gives the outcome probabilities

p (j) = ⟨ b_{j} ∣ ρ ∣ b_{j} ⟩ = Tr (ρ ∣ b_{j} ⟩ ⟨ b_{j} ∣) .

These probabilities are nonnegative by positive semidefiniteness and sum to one by the resolution of the identity and unit trace. In the computational basis, the answers are simply the diagonal entries

ρ_{jj}

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