Holevo's theorem says that no more than n bits can be stored (and retrieved) in n qubits. Indeed, allowing error can't improve this either -- the probability of retrieving the correct information is no better than that which could be transmitted in the same number of bits and guessing at the rest.
Superdense coding is one way around this bound: if the receiver shares n maximally entangled qubits with the sender, the sender can manipulate them such that when she gives the receiver her n qubits the receiver can obtain 2n bits of information. Perhaps this is not surprising, though, since he has to measure 2n qubits to get the data.
Is this the limit of quantum information capacity? That is, say sender and receiver share a large number N of entangled qubits and (after judicious manipulation and selection) the sender gives n of them to the receiver. Can more than 2n bits be transmitted in this way?
It would seem that the answer is "no", but I'd like a double-check. I'm very much a beginner, just working through Michael Nielsen's tutorials and Scott Aaronson's book. This question is similar to another question here but my question is different and not answered there.