I read that Shor's code is degenerate and, as consequence, an error $\sigma_{1}^z - \sigma_{2}^z$ annihilates codewords.

However, I also read that one can assume such kind of error to never occur, as not being part of the Pauli group.

Hence, I don't understand where is the problem on a code being degenerate.


1 Answer 1


I don't think there is particularly a problem with a code being degenerate. It's just important to know if a code is degenerate because it influences some of its properties. For example, some things like the Quantum Hamming Bound only apply to non-degenerate codes. It might also make decoding/error correction less obvious because there's not a one-to-one mapping between the errors that occur and error syndromes. As I say, this isn't actually a problem. It's more just a flag that says "be careful".


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