alexa Theory of quantum error correction for general noise
Bioinformatics & Systems Biology

Bioinformatics & Systems Biology

Journal of Computer Science & Systems Biology

Author(s): Knill E, Laflamme R, Viola L

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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. This article was published in Phys Rev Lett and referenced in Journal of Computer Science & Systems Biology

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