I apologize if this is a really silly question.
In the (textbook) quantum teleportation algorithm, in the step right after Alice has measured her system but before she has sent her classical information to Bob, she is about to send one of the following values: 00,01,10,11.
What if Bob doesn't want to wait and simply takes a guess? Wouldn't there then be superluminal communication 25% of the time?
Answer
This is really a subtle point. You are right that in 25% of the cases, Bob will randomly chose the "correct" measurement basis and thus get the correct value.
However, there is no way for Bob to know when he has actually chosen the right basis and when he has chosen the wrong basis, so his measurement outcome does not contain more information that a random coin-toss.
It is only when the information from Alice (regarding which basis to measure in) has reached him, that he can make use of his earlier (75% erroneous) measurements.
It is in this sence that information cannot propagate faster than the speed of light.
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