Formulating Quantum Theory as a Causally Neutral Theory of Bayesian Inference

          @misc{ pirsa_PIRSA:11110114,
            doi = {10.48660/11110114},
            url = {https://pirsa.org/11110114},
            author = {Spekkens, Robert},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Formulating Quantum Theory as a Causally Neutral Theory of Bayesian Inference},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {nov},
            note = {PIRSA:11110114 see, \url{https://pirsa.org}}
          }
          

Abstract

Quantum theory can be thought of as a noncommutative generalization of Bayesian probability theory, but for the analogy to be convincing, it should be possible to describe inferences among quantum systems in a manner that is independent of the causal relationship between those systems. In particular, it should be possible to unify the treatment of two kinds of inferences: (i) from beliefs about one system to beliefs about another, for instance, in the Einstein-Podolsky-Rosen or "quantum steering" phenomenon, and (ii) from beliefs about a system at one time to beliefs about that same system at another time, for instance, in predictions or retrodictions about a system undergoing dynamical evolution or undergoing a measurement. I will present a formalism that achieves such a unification by making use of "conditional quantum states", a noncommutative generalization of conditional probabilities. I argue for causal neutrality by drawing a comparison with a classical statistical theory with an epistemic restriction. (Joint work with Matthew Leifer).