Group Representations, Error Bases and Quantum Codes
Quantum Physics
2007-05-23 v1
Abstract
This report continues the discussion of unitary error bases and quantum codes begun in "Non-binary Unitary Error Bases and Quantum Codes". Nice error bases are characterized in terms of the existence of certain characters in a group. A general construction for error bases which are non-abelian over the center is given. The method for obtaining codes due to Calderbank et al. is generalized and expressed purely in representation theoretic terms. The significance of the inertia subgroup both for constructing codes and obtaining the set of transversally implementable operations is demonstrated.
Cite
@article{arxiv.quant-ph/9608049,
title = {Group Representations, Error Bases and Quantum Codes},
author = {E. Knill},
journal= {arXiv preprint arXiv:quant-ph/9608049},
year = {2007}
}
Comments
11 pages, preliminary report