Qubit Spin Convention: |0> & |1> Eigenvectors?

[lewis198]

This is a bit embarrassing, but by convention does $|0> = (1,0)^T$ and
$|1>=(0,1)^T$, where we are in the basis of the eigenvectors of $\sigma_{z}$?

 

[fzero]

The notation is a bit misleading, since $|0\rangle$ is most commonly used to denote the ground state of a system. However, in the absence of an external field, both spin states have the same energy. The justification for using the notation is the convention that in a communications protocol, one state must be chosen to signal binary 0 vs binary 1 for the other state. There's no particular reason to choose one over the other, but indeed the spin up state is conventionally chosen to be the off bit, see http://en.wikipedia.org/wiki/Qubit#Physical_representation