# Maximum number of bits in one single qubit? [duplicate]

How many bits can a qubit hold? I know there are probabilities involved in a qubit, but there must be some limit to how many bits a qubit can take. If different qubits can have different amounts of information then we can think of these as different sizes of processor-registers: $$8$$-bit, $$16$$-bit, $$32$$-bit or $$64$$-bit, can't we?

But my question is really, is there a limit to how much information content (discreete-wise) a qubit can store?

If you have $$N$$ classical bits of information, and wish to send them using qubits from $$A$$ to $$B$$, in such a way that $$B$$ can confidently reconstruct what the classical information was, say by writing it down in a book, then you will need $$N$$ qubits.
The second part is that qubits are nevertheless much more subtle than classical bits and can be used to perform a greater variety of information tasks. There are examples of information processing tasks where we have good reason to think that, to get a given outcome, if $$n$$ qubits are required then of order $$2^n$$ classical bits are required. It is not possible to prove this (because of a difficulty in computer science: we don't know how to rule out the possibility of very clever classical algorithms that might be discovered one day), but there is good reason to think that it is a true statement.