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arXiv:quant-ph/0510116

Comment on "Operator Quantum Error Correction"

Gerald N. Gilbert, Michael Hamrick, F. Javier Thayer, Yaakov S. Weinstein

Published Oct 17, 2005• 0 citations
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Abstract

The attempt to equate operator quantum error correction (quant-ph/0504189v1) with the quantum computer condition (quant-ph/0507141) in version two of quant-ph/0504189 is shown to be invalid.
DOI
10.48550/arxiv.quant-ph/0510116

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In a recent paper ([1]=quant-ph/0606035) it is shown how the optimal recovery operation in an error correction scheme can be considered as a semidefinite program. As a possible future improvement it is noted that still better error correction might be obtained by optimizing the encoding as well. In this note we present the result of such an improvement, specifically for the four-bit correction of an amplitude damping channel considered in [1]. We get a strict improvement for almost all values of the damping parameter. The method (and the computer code) is taken from our earlier study of such correction schemes (quant-ph/0307138).
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