dorsal/arxiv
View SchemaQuantum error-correcting codes associated with graphs
| Authors | D. Schlingemann, R. F. Werner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0012111 |
| URL | https://arxiv.org/abs/quant-ph/0012111 |
| DOI | 10.1103/PhysRevA.65.012308 |
Abstract
We present a construction scheme for quantum error correcting codes. The basic ingredients are a graph and a finite abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph such that the resulting code corrects a certain number of errors. This allows a simple verification of the 1-error correcting property of fivefold codes in any dimension. As new examples we construct a large class of codes saturating the singleton bound, as well as a tenfold code detecting 3 errors.
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"abstract": "We present a construction scheme for quantum error correcting codes. The\nbasic ingredients are a graph and a finite abelian group, from which the code\ncan explicitly be obtained. We prove necessary and sufficient conditions for\nthe graph such that the resulting code corrects a certain number of errors.\nThis allows a simple verification of the 1-error correcting property of\nfivefold codes in any dimension. As new examples we construct a large class of\ncodes saturating the singleton bound, as well as a tenfold code detecting 3\nerrors.",
"arxiv_id": "quant-ph/0012111",
"authors": [
"D. Schlingemann",
"R. F. Werner"
],
"categories": [
"quant-ph",
"cs.IT",
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"math.IT",
"math.MP"
],
"doi": "10.1103/PhysRevA.65.012308",
"title": "Quantum error-correcting codes associated with graphs",
"url": "https://arxiv.org/abs/quant-ph/0012111"
},
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