= Nondegenerate quantum error-correcting code
= Nondegenerate quantum code
{synonym}
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.
Back to article page
