= Projective state exclusion
{title2=$\langle b_j|\psi_j\rangle=0$}
For $d$ labelled <pure states> in dimension $d$, an <orthonormal basis> $\{|b_j\rangle\}_{j=0}^{d-1}$ supplies error-free <projective state exclusion> when $\langle b_j|\psi_j\rangle=0$ for every $j$. The <Born rule> gives zero <probability> to reporting $j$ on input $\psi_j$; orthonormal-basis completeness ensures that an outcome is always obtained. Conversely, zero error for this labelled <basic measurement> forces precisely those zero overlaps. The matrix of transition <probabilities> is therefore a matrix of column <probability distributions> with zero diagonal.
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