Guided tour · Error correction · step 6 of 11
The failure a syndrome cannot show
Some errors leave no trace at all, and that is precisely what a code's distance measures.
First, commit to an answer
Which is more dangerous: an error the decoder corrects wrongly, or one it never sees?
Decide before you follow the link. Nothing is recorded — the value is in having been wrong on purpose once.
Now go and look
Apply a Z error to the repetition code, then apply X and Y to the same qubit and compare all three verdicts.
What you should see
One qubit, three errors, three different fates: X is corrected, Y is miscorrected, and Z produces a blank syndrome while changing the logical state. That is why this code has distance 1 despite correcting every bit flip.