Degenerate coding for Pauli channels
Graeme Smith, John A. Smolin · arXiv (Cornell University) · 2006
One of the most striking features of quantum error correcting codes is that they can sometimes be used to correct more errors than they can uniquely identify. That is, quantum codes may be degenerate. We study a family of such codes and show they can be used to communicate over almost any Pauli channel at rates which are impossible for a nondegenerate code and which exceed those of previously known degenerate codes. We also identify a channel for which none of our codes outperforms the best nondegenerate code and show that it is nevertheless quite unlike any channel for which nondegenerate codes are known to be optimal.