= Binary rank-one qubit POVM
{title2=$E_1=(I+\mathbf n\cdot\boldsymbol\sigma)/2,\quad E_2=(I-\mathbf n\cdot\boldsymbol\sigma)/2$}
Two positive rank-one effects summing to $I$ in dimension two must be complementary <orthogonal projections>. Write the first as $\alpha|\psi\rangle\langle\psi|$ with normalized $\psi$. The second has eigenvalues $1-\alpha$ and $1$, so its rank-one condition forces $\alpha=1$. The two unit <Bloch vectors> are antipodal, and this <POVM> is a <projective measurement>.
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