= Correction implies detection at twice the weight
{title2=$\text{correct all weights }\leq t\ \Longrightarrow\ \text{detect all weights }\leq2t$}
Split the support of a <Pauli operator> of weight at most $2t$ into two sets of size at most $t$. It is, up to a scalar phase, $E_a^\dagger E_b$ for two errors in the correctable family. The <Knill--Laflamme condition> makes its compression to the code scalar, which is <quantum error detection>. Expansion in the Pauli basis extends the assertion to every operator supported on at most $2t$ <qubits>. The number $t$ counts affected qubits, not the cardinality of an arbitrary selected family of errors.
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