Journal
PHYSICAL REVIEW LETTERS
Volume 84, Issue 11, Pages 2525-2528Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.84.2525
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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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