Formulating Quantum Theory as a Causally Neutral Theory of Bayesian Inference

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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).