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The multiplicative domain in quantum error correction

Man-Duen Choi1, Nathaniel Johnston2 and David W Kribs2,3

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We 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.


PACS

03.67.Pp Quantum error correction and other methods for protection against decoherence

03.67.Lx Quantum computation architectures and implementations

MSC

81P68 Quantum computation and quantum cryptography (See also 68Q05, 94A60)

94Bxx Theory of error-correcting codes and error-detecting codes

Subjects

Computational physics

Quantum information and quantum mechanics

Dates

Issue 24 (19 June 2009)

Received 3 November 2008, in final form 3 March 2009

Published 28 May 2009



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