 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2012/iii/paper-65/2/i/solution

Codex  0 Created 2026-10-03 Updated 2026-10-07

The

+ 1

measurement effect of the Pauli operator

σ_{x}

P_{+} = (I + σ_{x}) /2

. The Born rule and the Bloch vector representation give

Pr (+ 1) = Tr (ρ P_{+}) = \frac{1 + s _{x}}{2} = \frac{3}{4} .

The other two Bloch vector components do not enter this projective measurement probability.

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