# Oblivious transfer impossible from noiseless channels

If computationally unbounded parties $$A$$ and $$B$$ have only a noiseless channel between them, why is information-theoretic oblivious transfer impossible even for the passive cheating setting?

Intuitively, the noiseless channel makes the views of $$A$$ and $$B$$ almost identical except for the private randomness that $$A$$ and $$B$$ use. An unbounded passive cheater shouldn't be able to guess this randomness. How do we provably rule out some clever usage of private randomness that allows the sender to hide one of their bits and the receiver to hide her choice bit?