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Phys Rev Lett. 2000 Mar 13;84(11):2525-8.

Theory of quantum error correction for general noise

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Los Alamos National Laboratory, MS B265, Los Alamos, New Mexico 87545, USA.


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.

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