Generalization of Quantum information?

Question

I've been working a lot with classical information theory results for my undergraduate thesis (thank you Shannon). At the same time, I am taking a course in quantum computing where we discuss briefly quantum information theory. I understand that the classical conception of information comes from the advent of electromechanical information sending and quantum information comes directly from quantum mechanics. I see these two fields as distinct but very closely related. My whole mathematical education so far has been showing me generalizations of generalizations (eg calculus becomes real/complex analysis which may become measure theory in some sense, etc). I'm curious if there is a rigorous definition of information from first principles which encompasses both classical and quantum information. Similar to how linear algebra can be derived from group theory/abstract algebra with certain structures and axioms, is there a meta understanding of information that encompasses both mainstream theories?