 Nondegenerate quantum error-correcting code

For a specified correctable set of distinct Pauli operators modulo phase, a nondegenerate code has mutually orthogonal error images $E\mathcal{X}$. Equivalently, the matrix in the Knill--Laflamme condition is diagonal for that Pauli error set. Each error therefore requires a separate syndrome subspace of dimension equal to the logical code dimension. Degenerate codes can have distinct errors with the same action on the code and do not satisfy this orthogonality counting argument.