Details
| Original language | English |
|---|---|
| Pages (from-to) | 012308 |
| Number of pages | 1 |
| Journal | Phys. Rev. A |
| Volume | 65 |
| Issue number | 1 |
| Publication status | Published - 2002 |
Abstract
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In: Phys. Rev. A, Vol. 65, No. 1, 2002, p. 012308.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Quantum error-correcting codes associated with graphs
AU - Schlingemann, D
AU - Werner, R. F.
PY - 2002
Y1 - 2002
N2 - We present a construction 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 one-error correcting property of codes of length 5 in any dimension. As examples, we construct a large class of maximum distance separable codes, i.e. codes saturating the Singleton bound, as well as a code of length 10 detecting three errors.
AB - We present a construction 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 one-error correcting property of codes of length 5 in any dimension. As examples, we construct a large class of maximum distance separable codes, i.e. codes saturating the Singleton bound, as well as a code of length 10 detecting three errors.
U2 - 10.1103/PhysRevA.65.012308
DO - 10.1103/PhysRevA.65.012308
M3 - Article
VL - 65
SP - 012308
JO - Phys. Rev. A
JF - Phys. Rev. A
SN - 2469-9934
IS - 1
ER -