Is quantum teleportation guessable?

Question

The only obstacle preventing quantum teleportation to break the speed of light (in terms of communication speed) is the need to use classical communication to tell the other party how to perform the quantum system's measurement.
I wonder if those classical communications could be guessed. It makes sense to say that the answer is yes if the amount of data transferred over the quantum teleportation channel is greater than the classical. Then even if it's not feasible to guess it in a short amount of time, it should at least be possible. While if the amount of data is of the same order, then guessing will not be possible because the noise will be far too great.
Here is an example setup to demonstrate to you what I mean.

Alice and Bob set up a quantum teleportation channel to exchange 1 GB of data (never mind the quBits to bytes conversion).
Alice needs to send Bob 1Kb of classical data to allow Bob to extract the 1 GB of quantum data.
Alice adds a checksum to the 1GB of data and sends a new message to Bob every minute
Bob makes one guess a minute to see if he got the checksum right

I assume that, in reality, things are more complicated from how I describe them here. Can you please explain how it works and if guessing the classical communication parts is possible?

glS · Answer

Very roughly speaking, quantum teleportation works as follows: Alice and Bob share an entangled state, call it $|Psirangle$. Alice wants to "send" Bob some state, call it $|psirangle$. To do it, she performs some operations on her part of the shared state, and then performs a measurement, obtaining some result (note that the result she gets is probabilistic, i.e. unpredictable).
Now Alice tells Bob, via a standard classical channel, the measurement result she obtained. Using this information, and assuming Bob and Alice previously coordinated so that they know which operations Alice was going to perform on her share of the state, Bob can use the information sent by Alice to figure out what operation to perform on his state to recover $|psirangle$.
This process is nontrivial because the information sent by Alice to Bob would not have been sufficient, on its own, to fully characterise $|psirangle$ (otherwise the task would have been trivial).
It is crucial to realize that the goal of quantum teleportation is to "transmit" a quantum state, not classical information. It is therefore not clear how your proposal would even apply. It doesn't make much sense to say that you are transmitting "1 GB of data".

Is quantum teleportation guessable?

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