Past exam of the mathematics course of the University of Cambridge / 2012 / iii / Paper 65 / 2 / i / Solution

The $+1$ measurement effect of the Pauli operator ${\sigma }_x$ is $P_{+}=(I+{\sigma }_x)/2$. The Born rule and the Bloch vector representation giveThe other two Bloch vector components do not enter this projective measurement probability.