 Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2021/quantum-information/1/a/i/solution

In an orthonormal computational basis, the squared norm is the sum of the squared moduli of the coefficients:

⟨ ϕ ∣ ϕ ⟩ = \frac{3}{2}^{2} + \frac{1 + i 3}{4}^{2} = \frac{3}{4} + \frac{1 + 3}{16} = 1 .

Thus the vector is normalized and represents a pure state of a qubit. The imaginary part contributes positively to the squared modulus; squaring the coefficient without complex conjugation would give the wrong norm.

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