dorsal/arxiv
View SchemaQuantum Stabilizer Codes and Classical Linear Codes
| Authors | Richard Cleve |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9612048 |
| URL | https://arxiv.org/abs/quant-ph/9612048 |
| DOI | 10.1103/PhysRevA.55.4054 |
Abstract
We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result -- which applies to degenerate as well as nondegenerate codes -- previously established necessary conditions for classical linear codes can be easily translated into necessary conditions for quantum stabilizer codes. Examples of specific consequences are: for a quantum channel subject to a delta-fraction of errors, the best asymptotic capacity attainable by any stabilizer code cannot exceed H(1/2 + sqrt(2*delta*(1-2*delta))); and, for the depolarizing channel with fidelity parameter delta, the best asymptotic capacity attainable by any stabilizer code cannot exceed 1-H(delta).
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"abstract": "We show that within any quantum stabilizer code there lurks a classical\nbinary linear code with similar error-correcting capabilities, thereby\ndemonstrating new connections between quantum codes and classical codes. Using\nthis result -- which applies to degenerate as well as nondegenerate codes --\npreviously established necessary conditions for classical linear codes can be\neasily translated into necessary conditions for quantum stabilizer codes.\nExamples of specific consequences are: for a quantum channel subject to a\ndelta-fraction of errors, the best asymptotic capacity attainable by any\nstabilizer code cannot exceed H(1/2 + sqrt(2*delta*(1-2*delta))); and, for the\ndepolarizing channel with fidelity parameter delta, the best asymptotic\ncapacity attainable by any stabilizer code cannot exceed 1-H(delta).",
"arxiv_id": "quant-ph/9612048",
"authors": [
"Richard Cleve"
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"quant-ph"
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"doi": "10.1103/PhysRevA.55.4054",
"title": "Quantum Stabilizer Codes and Classical Linear Codes",
"url": "https://arxiv.org/abs/quant-ph/9612048"
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