georgir said:
Doesn't quantum teleportation show us that there are in fact at most 4 possible quantum states for a single qbit?
Superdense coding, which transmit 2 bits (i.e. one of four states) via a single pre-entangled qubit, is a much better example of your point than quantum teleportation.
Technically you can encode any finite number of states into a single qubit, since it has a continuous state space instead of a discrete state space. The problem comes when you want to read the information back out, and you need to
distinguish those states. That's where you're really limited to ##2^n## states for ##n## qubits.
Superdense coding and quantum teleportation can use and distinguish four states only because they involve two qubits. It's
interesting and
useful that you can write all four states using just one of the qubits involved in a bell pair, but reading what you wrote still requires combining both qubits and there's no way to make it work without that second qubit around.
Personally, I often find myself thinking of a qubit as being "worth" up to two bits, but it's important to understand that this is an intuition that breaks down in many cases (e.g. you need pre-existing entanglement).
*edit*: I think I inverted the meaning of your question, and answered "Doesn't QT mean a single qubit can hold 4 distinguishable states?". The answer to your actual question is that it's kind of complicated what you can and can't put in qubits, but we do know that 2 bits per qubit is an absolute maximum when it comes to transmitting classical information over a quantum channel (even with arbitrary pre-existing entanglement). This is different from "qubits can hold at most 4 states" though. The state space of a qubit is continuous, not discrete, and our predictions about how they behave would be wrong if we tried to reduce that down to just 4 points.
