Abstract: In this talk\, I will present a novel\, exact correspondence between stochastic-process theory and quantum theory. On the one hand\, this stochastic-quantum correspondence means that one can use the Hilbert-space tools of quantum theory to model real-world stochastic processes beyond the usual Markov approximation\, generalizing previous stochastic approaches to quantum theory as well as potentially opening up new applications for quantum simulators and quantum computers. On the other hand\, the stochastic-quantum correspondence implies that one can replace the instrumentalist textbook axioms of quantum theory with much more physically transparent axioms. The result is a clearer physical picture underlying quantum theory that is consistent with the standard no-go theorems\, helps clarify the meaning of signature features of quantum theory like interference and entanglement\, and has potential implications for addressing the measurement problem.

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