A quantum code corrects a noise subspace exactly when that subspace admits a special basis of partial isometries with orthogonal ranges, a criterion equivalent to Knill-Laflamme but with new structural consequences.
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Quantum error-correcting codes via inner products and error bases
A quantum code corrects a noise subspace exactly when that subspace admits a special basis of partial isometries with orthogonal ranges, a criterion equivalent to Knill-Laflamme but with new structural consequences.