Solution
= Solution
The <spectral projector> for outcome $+1$ is
$$
\Pi_+=\frac{I+A}{2}.
$$
For $|1\rangle=(0,1)^T$, the <Born rule> gives
$$
\mathbb P(+1)
=\langle1|\Pi_+|1\rangle
=\frac{1-n_z}{2}
=\boxed{\sin^2\frac\theta2}.
$$
= Solution
The <spectral projector> for outcome $+1$ is
$$
\Pi_+=\frac{I+A}{2}.
$$
For $|1\rangle=(0,1)^T$, the <Born rule> gives
$$
\mathbb P(+1)
=\langle1|\Pi_+|1\rangle
=\frac{1-n_z}{2}
=\boxed{\sin^2\frac\theta2}.
$$