I have two question concerning information content of qubit.
Question 1: How many classical bits are needed to represent a qubit:
A qubit can be represented by a vector $q = \begin{pmatrix}\alpha \\\beta \end{pmatrix}, ~~ \alpha, \beta \in \mathbb{C}$. So, we need four real numbers to represent it. But when facts that (i) $|\alpha|^2+|\beta|^2 = 1$ and (ii) two qubits which differ in global phase only are indistinguishable, are taken into account, only two real numbers are necessary (angles on Bloch sphere). Moreover, we can choose a precission of the qubit representation (i.e. number of decimal places in $\alpha$ and $\beta$ or Bloch sphere angles) which influence number of classical bits needed to described the qubit.
So, it seems to me that the qubit representation cannot be used for measuring qubit information content but only memory consumption in simulation. Am I right?
Question 2: What is an (effective) information content of qubit:
A superdense coding enable us to send two classical bits via one qubit. But on the other hand you need two entangled qubits prepared in advance.
Given these facts, what is an information content of qubit? One or two classical bits? Or do I need to use another angle of view given the fact that qubits are "continuous" (i.e. described by complex numbers $\alpha$ and $\beta$)?