  We study the approximate correctability of general algebras of observables,
which represent hybrid quantum-classical information. This includes approximate
quantum error correcting codes and subsystems codes. We show that the main
result of arXiv:quant-ph/0605009 yields a natural generalization of the
Knill-Laflamme conditions in the form of a dimension independent estimate of
the optimal reconstruction error for a given encoding, measured using the
trace-norm distance to a noiseless channel.
