# Phase flip error correction on state $|0\rangle$

When I read documentations about quantum error correction, it generally speak about bit flip error, and phase flip on $$|1\rangle$$ state, so for example, let's say my initial state is $$|\psi\rangle = a|0\rangle+b|1\rangle$$, bit flip error correction $$|\psi'\rangle = b|0\rangle+a|1\rangle$$ or phase flip error correction $$|\psi'\rangle = a|0\rangle-b|1\rangle$$.

I'm wondering why the phase flip error correction $$|\psi'\rangle = -a|0\rangle+b|1\rangle$$ is never discussed? And why error correction codes don't correct this phase flip (at least these I have tested)? Is there a reason I'm not aware about ? Maybe this error never happens "in real life"?

The bit- and phase-flip error you are asking for, i.e. $$|\psi'\rangle = b|0\rangle-a|1\rangle$$ does indeed exist, and error correction for them have been constructed. The phase flip is associated to the $$Z$$ Pauli matrix and the bit flip to the $$X$$ pauli matrix. The error you are asking for is associated to the $$Y$$ pauli matrix. Not that its action is $$Y|\psi\rangle=-i(b|0\rangle-a|1\rangle)$$, but as it has been stated in the other answers, the global phase has not observational consequences, and such error would be the one you are aksing for.
I recommend this article for a better understanding of the decoherence models. In such you can see discussions about the Pauli channel (a channel with errors $$X,Y,Z$$) and also an example of a QECC that does indeed correct all of those kinds of errors with weight one.
An error that negates the amplitude of $$|0\rangle$$ is observationally indistinguishable from an error that negates the $$|1\rangle$$ state, so there's no need to consider both. By arbitrary historical convention the Z gate negates the $$|1\rangle$$ state and so things are done in those terms.
The difference between $$a|0\rangle-b|1\rangle$$ and $$-a|0\rangle+b|1\rangle$$ is a global phase which has no observational consequences. In other words, to all intents and purposes, those two errors $$Z$$ and $$-Z$$ are the same. An error correcting code that corrects for one also corrects for the other (although the global phase may remain).