Demarcating probability theories by their degree of agent-dependency

          @misc{ pirsa_PIRSA:09080020,
            doi = {10.48660/09080020},
            url = {https://pirsa.org/09080020},
            author = {Rau, Jochen},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Demarcating probability theories by their degree of agent-dependency},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {aug},
            note = {PIRSA:09080020 see, \url{https://pirsa.org}}
          }
          

Abstract

Recent advances in quantum computation and quantum information theory have led to revived interest in, and cross-fertilisation with, foundational issues of quantum theory. In particular, it has become apparent that quantum theory may be interpreted as but a variant of the classical theory of probability and information. While the two theories may at first sight appear widely different, they actually share a substantial core of common properties; and their divergence can be reduced to a single attribute only, their respective degree of agent-dependency. I propose a mathematical description for this ?degree of agent-dependency? and show how assuming different values allows one to derive the classical and the quantum case from their common core. Finally, I explore ? and eventually dismiss ? the possibility that beyond quantum theory there might be other variants of classical probability theory that are relevant to physics.