Theory of Quantum Error Correction for General Noise

Emanuel Knill; Raymond Laflamme; Lorenza Viola

doi:10.1103/PhysRevLett.84.2525

Theory of Quantum Error Correction for General Noise

Emanuel Knill, Raymond Laflamme, and Lorenza Viola

Phys. Rev. Lett. 84, 2525 – Published 13 March 2000

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.

Received 10 September 1999

DOI:https://doi.org/10.1103/PhysRevLett.84.2525

Authors & Affiliations

Emanuel Knill^1,*, Raymond Laflamme^1,†, and Lorenza Viola^2,‡

¹Los Alamos National Laboratory, MS B265, Los Alamos, New Mexico 87545
²d'Arbeloff Laboratory for Information Systems and Technology, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

^*Electronic address: knill@lanl.gov
^†Electronic address: laflamme@lanl.gov
^‡Electronic address: vlorenza@mit.edu