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arXiv:math/0405032 · Journal of Mathematical Physics

Universal collective rotation channels and quantum error correction

Marius Junge, Peter T. Kim, David W. Kribs

Published Jan 26, 2005• 9 citations
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Abstract

We present and investigate a new class of quantum channels, what we call “universal collective rotation channels,” that includes the class of collective rotation channels as a special case. The fixed point set and noise commutant coincide for a channel in this class. Computing the precise structure of this C*-algebra is a core problem in a particular noiseless subsystem method of quantum error correction. We prove that there is an abundance of noiseless subsystems for every channel in this class and that the Young tableaux combinatorial machine may be used to explicitly compute these subsystems.

DOI
10.1063/1.1824213

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We present and investigate a new class of quantum channels, what we call “universal collective rotation channels,” that includes the class of collective rotation channels as a special case. The fixed point set and noise commutant coincide for a channel in this class. Computing the precise structure of this C*-algebra is a core problem in a particular noiseless subsystem method of quantum error correction. We prove that there is an abundance of noiseless subsystems for every channel in this class and that the Young tableaux combinatorial machine may be used to explicitly compute these subsystems.
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This paper is an expanded and more detailed version of our recent work in which the Operator Quantum Error Correction formalism was introduced. This is a new scheme for the error correction of quantum operations that incorporates the known techniques - i.e. the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method - as special cases, and relies on a generalized mathematical framework for noiseless subsystems that applies to arbitrary quantum operations. We also discuss a number of examples and introduce the notion of ``unitarily noiseless subsystems''.
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