Group Representations, Error Bases and Quantum Codes
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چکیده
This report continues the discussion of unitary error bases and quantum codes begun in 8]. 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. 2] is generalized and expressed purely in representation theoretic terms. The signiicance of the inertia subgroup both for constructing codes and obtaining the set of transversally implementable operations is demonstrated. 1 Overview This report discusses the construction of quantum codes based on nice error bases 8]. The main conclusion is that much of the relevant theory can be cast in terms of representations of nite groups. It is shown that nice error bases are equivalent to the existence of an irreducible character with non-zero values only on the center. The technique for obtaining codes 1
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