Group Representations, Error Bases and Quantum Codes

Details Group Representations, Error Bases and Quantum Codes Group Representations, Error Bases and Quantum Codes

1996-08-29

arxiv.org/abs/quant-ph/9608049v1

Physics

Quantum Physics

11 pages, preliminary report

Scientific paper

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.

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