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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?

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There is a natural and direct link between information theory and quantum theory in the Quantum Entropic Uncertainty Principle. This area of study stems from a conjecture made by one of Wheeler's PhD students, Hugh Everett III, in 1957 while working on his thesis, which introduced the formalism of MWI.

Everett's conjecture was proven in 1975. In the late 70's David Deutsch was a student at UT Austin with Wheeler, and met Everett when he came to give a seminar. In 1985 Deutsch published his landmark paper Quantum theory, the Church-Turing principle and the universal quantum computer. This paper introduced the quantum circuit model that we still use today, and it relies heavily on Everett's formulation of quantum mechanics (MWI).

It's a testament to Wheeler's foresight and pedagogy that he saw this as a productive direction to push his students. Whether one views it as natural or not, it was certainly highly productive. Wheeler was both brilliant and highly creative, and he was generally happy to socialize creative theories before he could rigorously support them. According to Feynman${}^\dagger$ (another of Wheeler's PhD students) one the critical insights that led to his path integral formulation resulted from Wheeler informing him of his conclusion that there was only a single electron in the universe.

${}^\dagger$ If you don't want to read the whole Nobel Lecture, search "Because, they are all the same electron!"

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