 Solution

ID: past-exam-of-the-laser-science-and-quantum-information-processing-course-of-the-university-of-oxford/2019/4/c/iii/solution

Complete the square:

F = 2 (p - 1/2)^{2} + 1/2

. Therefore

F_{m i n} = \frac{1}{2}, ∣ ψ ⟩ = \frac{∣0 ⟩ + e ^{i φ} ∣1 ⟩}{2} .

Every equatorial Bloch-sphere state attains the minimum, not just

∣ + ⟩

and

∣ - ⟩

. Its unread Z measurement gives

I /2

, having removed all information contained in its relative phase.

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