 Solution

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

Expand the density matrix of the Bell state and take the partial trace over Alice's qubit:

∣ ϕ_{+} ⟩ ⟨ ϕ_{+} ∣ = \frac{1}{2} \sum_{j, k = 0}^{1} ∣ j ⟩ ⟨ k ∣_{A} \otimes ∣ j ⟩ ⟨ k ∣_{B}, ρ_{B} = \frac{1}{2} \sum_{j, k = 0}^{1} ⟨ k ∣ j ⟩ ∣ j ⟩ ⟨ k ∣.

ρ_{B} = \frac{1}{2} (∣0 ⟩ ⟨ 0∣ + ∣1 ⟩ ⟨ 1∣) = \frac{I}{2} .

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