 Solution

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

Since

F = 1 - 2 p (1 - p)

with

0 \leq p \leq 1

, its maximum occurs at

p = 0

p = 1

F_{m a x} = 1, ∣ ψ ⟩ = ∣0 ⟩ or ∣1 ⟩

up to a global phase. These are the eigenstates of the measured observable, so their ideal measurement does not disturb them.

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