Quantum error-correcting codes associated with graphs
Quantum Physics
2013-05-29 v1 Information Theory
Mathematical Physics
math.IT
math.MP
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.
Cite
@article{arxiv.quant-ph/0012111,
title = {Quantum error-correcting codes associated with graphs},
author = {D. Schlingemann and R. F. Werner},
journal= {arXiv preprint arXiv:quant-ph/0012111},
year = {2013}
}
Comments
8 pages revtex, 5 figures