1980s. John Wheeler at the University of Texas would tell his students, “Give an information theoretic derivation of quantum theory!” Information theoretic is an adjective for Claude Shannon's information theory, which used log probabilities to represent bits.
With this desperate call to make quantum theory relatable to information theory, or molded in its likeness, is the link between Shannon's information theory unnaturally linked to "quantum theory of information"? In other words, is the connection between them man-made (superficial) and quantitatively contrived? or are classical and quantum information naturally bonded?
What did Wheeler's career conclude about the connection between information theory and quantum theory (quantum information)? Was he able to derive it information theoretically, and what exactly is the derivation?