Binary rank-one qubit POVM ($E_1=(I+\mathbf{n}\cdot \mathbf{\sigma })/2,E_2=(I-\mathbf{n}\cdot \mathbf{\sigma })/2$)

Two positive rank-one effects summing to $I$ in dimension two must be complementary orthogonal projections. Write the first as $\alpha |\psi ⟩⟨\psi |$ 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.