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Approximate Operator Quantum Error Correction
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Title  Approximate Operator Quantum Error Correction 
Title of Series  Second International Conference on Quantum Error Correction (QEC11) 
Author 
Mandayam, Prabha

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CC Attribution  NonCommercial  NoDerivatives 3.0 Germany: You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and noncommercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
DOI  10.5446/35288 
Publisher  University of Southern California (USC) 
Release Date  2011 
Language  English 
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Subject Area  Computer Science, Mathematics, Physics 
Abstract  Operator quantum error correction (OQEC) extends the standard formalism of quantum error correction (QEC) to codes in which only a subsystem within a subspace of states is used to store information in a noiseresilient fashion. Motivated by recent work on approximate QEC, which makes it possible to construct subspace codes beyond the framework of perfect error correction, we investigate the problem of approximate operator quantum error correction (AOQEC). We demonstrate easily checkable sufficient conditions for the existence of approximate subsystem codes. Furthermore, we prove the efficacy of the transpose channel as a simpletoconstruct recovery map that works nearly as well as the optimal recovery channel, with optimality defined in terms of worstcase fidelity over all code states. This work generalizes our earlier approach of using the transpose channel for approximate subspace correction to the case of approximate OQEC, thus bringing us closer to a full analytical understanding of approximate codes. 
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