So, right now these are two pieces of information I've been told are correct:
- Quantum teleportation can send a single qubit from Alice to Bob, with two classical bits
- $n$ qubits can store $2^n$ classical bits of information
If both of these are true, using, for example, 16 classical bits and 8 preshared qubits, could Alice send Bob 256 classical bits of information via teleportation?
My understanding is that both teleportation (which I understand fairly well) and storing exponentially many bits with multiple qubits (which I don't know much about) involve entanglement. Would this mean that these two properties are sort of mutually exclusive, and you can only have one at once (preventing more than 2 classical bits/qubit from being sent through teleportation)? Or is it indeed possible to send exponentially more data through a classical communication channel by presharing qubits for teleportation?