On the Structure of Additive Quantum Codes and the Existence of Nonadditive Codes
نویسندگان
چکیده
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− 2H2(2t/n), where H2(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.
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