title: Theory of quantum error correction for general noise
abstract: A measure of quality of an error-correcting code is the maximum number of errors that it is able to correct. We show that a suitable notion of "number of errors" e makes sense for any quantum or classical system in the presence of arbitrary interactions. Thus, e-error-correcting codes protect information without requiring the usual assumptions of independence. We prove the existence of large codes for both quantum and classical information. By viewing error-correcting codes as subsystems, we relate codes to irreducible representations of operator algebras and show that noiseless subsystems are infinite-distance error-correcting codes.
authors.affiliation: Los Alamos National Laboratory, MS B265, Los Alamos, New Mexico 87545, USA.
authors.initials: E
authors.lastname: Knill
authors.initials: R
authors.lastname: Laflamme
authors.initials: L
authors.lastname: Viola