Title :
Graphs, quadratic forms, and quantum codes
Author :
Grassl, Markus ; Klappenecker, Andreas ; Rötteler, Martin
Author_Institution :
Inst. fur Algorithmen und Kognitive Syst., Karlsruhe Univ., Germany
Abstract :
We show that any stabilizer code over a finite field is equivalent to a graphical quantum code. Furthermore we prove that a graphical quantum code over a finite field is a stabilizer code. The technique used in the proof establishes a new connection between quantum codes and quadratic forms.
Keywords :
error correction codes; graph theory; quantum communication; additive group; error-correcting codes; finite field; graphical quantum code; quadratic forms; stabilizer code; undirected graph; Computer science; Contracts; Eigenvalues and eigenfunctions; Galois fields; Hamming weight; Quantum computing; Quantum mechanics; Symmetric matrices;
Conference_Titel :
Information Theory, 2002. Proceedings. 2002 IEEE International Symposium on
Print_ISBN :
0-7803-7501-7
DOI :
10.1109/ISIT.2002.1023317
