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arXiv:quant-ph/9710031

On the Structure of Additive Quantum Codes and the Existence of Nonadditive Codes

Vwani Roychowdhury, Farrokh Vatan

Published Oct 9, 1997• 4 citations

Abstract

We first present a useful characterization of additive (stabilizer) quantum error-correcting codes. Then we present several examples of We first present a useful characterization of additive (stabilizer) quantum error--correcting codes. Then we present several examples of nonadditive codes. We show that there exist infinitely many non-trivial nonadditive codes with different minimum distances, and high rates. In fact, we show that nonadditive codes that correct t errors can reach the asymptotic rate R=1-2H(2t/n), where H(x) is the binary entropy function. Finally, we introduce the notion of strongly nonadditive codes (i.e., quantum codes with the following property: the trivial code consisting of the entire Hilbert space is the only additive code that is equivalent to any code containing the given code), and provide a construction for an ((11,2,3)) strongly nonadditive code.

DOI: 10.48550/arxiv.quant-ph/9710031

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