= Tetrahedral qubit POVM
{title2=$E_i=\frac14(I+\mathbf n_i\cdot\boldsymbol\sigma)$}
Choose the four unit <Bloch vectors> at the vertices of a <regular tetrahedron>, so $\sum_i\mathbf n_i=0$ and $\sum_i\mathbf n_i\mathbf n_i^T=4I/3$. The displayed four positive rank-one effects sum to $I$. On input $(I+\mathbf r\cdot\boldsymbol\sigma)/2$, their probabilities are $p_i=(1+\mathbf r\cdot\mathbf n_i)/4$, giving the reconstruction $\mathbf r=3\sum_i p_i\mathbf n_i$. This realizes the smallest fixed qubit <informationally complete POVM>.
Back to article page
