Comment on "Optimum Quantum Error Recovery using Semidefinite  Programming"

M. Reimpell; R. F. Werner; K. Audenaert

Comment on "Optimum Quantum Error Recovery using Semidefinite Programming"

M. Reimpell, R. F. Werner, K. Audenaert

Department of Mathematics

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Abstract

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).

Original language	English
Publisher	Unkown Publisher
Publication status	Published - 7 Jun 2006

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quant-ph

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abstract = "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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AU - Werner, R. F.

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Y1 - 2006/6/7

N2 - 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).

AB - 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).