Is a theoretically secure key exchange possible?
I believe you are talking about the existence of information-theoretically (unconditionally) secure key agreement schemes. You can prove that such schemes cannot be achieved with only authenticated channels from Alice to Bob and Bob to Alice.

Nevertheless, if Alice, Bob, and Eve are in possession of some sort of correlated randomness, then it may be possible to construct such a scheme. 

One such example is when a satellite broadcasts several random bits, and Alice, Bob, and Eve receive the bits through different binary symmetric channels with certain error probabilities. One can prove that, in this case, information-theoretical key agreement is possible, even when Eve's error probability is much lower than Alice's and Bob's.

A classic paper on this topic is "Secret Key Agreement by Public Discussion from Common Information" by Ueli Maurer.