I Clarification on what we can consider a qubit to be

[eprparadox]

In a 2 level quantum system, should I consider the states

|0>

and

|1|>

to be qubits by themselves?

Or is only the SUPERPOSITION of these two states,

\alpha |0> + \beta |1>

considered to be a qubit?

 

[eprparadox]

Nevermind, they have to be qubits as well. If we consider our superposition to be a qubit, then we can set $\alpha = 1$ and $\beta = 0$ and that should be an appropriate qubit state.

 

[A. Neumaier]

In a 2 level quantum system, should I consider [...] to be qubits by themselves?

The qubit is the 2-state system, just like a classical bit is a binary variable. The states are not qubits, but the qauntum analogues of the classical values.

 

[Strilanc]

You should consider the pair to form a qubit. On their own they're not very useful.

Another useful way to think about what a qubit is is as an anti-commuting pair of observables, such as the observable $|0\rangle$-vs-$|1\rangle$ paired with the observable $\frac{1}{\sqrt{2}} \left( |0\rangle + |1\rangle \right)$-vs-$\frac{1}{\sqrt{2}} \left( |0\rangle - |1\rangle \right)$.