Proposition: A truth-table error can be maximal

If $f\ne h$, then their bit-oracle channels satisfy

This can occur when their truth tables disagree at only one address.

Proof. Choose $x$ with $f(x)\ne h(x)$. The input $|x⟩|0⟩$ produces orthogonal output basis states, so the half-diamond distance is at least one. One is also its universal upper bound.