Access classification

For a Pauli error, its syndrome is the four-bit vector recording anticommutation with $g_1,\dots ,g_4$. The single-qubit syndromes are:

They are precisely the fifteen distinct nonzero four-bit vectors. Every nonidentity Pauli of weight one or two therefore has nonzero syndrome. For weight two, this follows because its syndrome is the sum of two distinct single-site syndromes.