What does this equation mean?

The technique that makes this work is the stabiliser formalism, given its general fault-tolerant treatment by Gottesman [ 4 ] . A code is defined not by listing its states but by naming a set of commuting Pauli operators $S_i$ — the stabiliser generators — whose joint +1 eigenspace is the code space: $S_i \, |\psi_L\rangle = + |\psi_L\rangle , \qquad i = 1, \dots, n - k$. An [[n, k, d]] code encodes k logical qubits into n physical qubits with distance d . The stabiliser generators are measured repeatedly. Because each $S_i$ commutes with every other and with the logical operators, measuring them extracts no information about which encoded state is present. What it extracts is whether an error has anticommuted with a given check — a single classical bit per generator, per round. That bit string is the syndrome.