 Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2020/quantum-information/3/b/i/solution

⟨ e_{0} ∣ x ⟩ = \frac{1}{N} \sum_{y = 0}^{N - 1} ⟨ y ∣ x ⟩ = \frac{1}{N} \sum_{y = 0}^{N - 1} δ_{y x} = \frac{1}{N} .

There is one nonzero term, the term with

y = x

. In particular, the uniform coefficient is unchanged when passing from the ket to its bra because it is real.

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