2
$\begingroup$

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.

$\endgroup$

1 Answer 1

4
$\begingroup$

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".

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.