Man-Duen Choi et al 2009 J. Phys. A: Math. Theor. 42 245303 doi:10.1088/1751-8113/42/24/245303
Man-Duen Choi1, Nathaniel Johnston2 and David W Kribs2,3
Show affiliationsWe show that the multiplicative domain of a completely positive map yields a new class of quantum error correcting codes. In the case of a unital quantum channel, these are precisely the codes that do not require a measurement as part of the recovery process, the so-called unitarily correctable codes. In the arbitrary, not necessarily unital case, they form a proper subset of unitarily correctable codes that can be computed from the properties of the channel. As part of the analysis, we derive a representation theoretic characterization of subsystem codes. We also present a number of illustrative examples.
03.67.Pp Quantum error correction and other methods for protection against decoherence
03.67.Lx Quantum computation architectures and implementations
81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)
94Bxx Theory of error-correcting codes and error-detecting codes
Issue 24 (19 June 2009)
Received 3 November 2008, in final form 3 March 2009
Published 28 May 2009
Man-Duen Choi et al 2009 J. Phys. A: Math. Theor. 42 245303
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