 Quantum error detection

A code with orthogonal projector $P$ detects an error $E$ when its compression to the code is scalar. A projective measurement of $P$ then either flags departure from the code or, on a successful code-space outcome, leaves the logical state unchanged up to normalization. This includes harmless scalar errors, even though they need not produce a nonzero error syndrome. Detectability extends by linearity to the span of a set of errors. Every Pauli operator of weight less than the quantum code distance is detectable.