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Towards a Framework of Probabilistic Bayesian Theories

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Quantum mechanics can be seen as a set of instructions how to calculate probabilities by associating mathematical objects to physical procedures, like preparation, manipulation, and measurement of a system. Quantum theory then yields probabilities which are neutral with respect to its use, e.g., in a Bayesian or a frequentistic way. We investigate a different approach to quantum theory and physical theories in general, in which we aim for subjective predictions in the Bayesian sense. This gives a structure different from the operational framework of general probabilistic theories. We explore these differences and the according mathematical language of such probabilistic Bayesian theories. This is joint work with Adan Cabello, Giulio Chiribela, and Markus Müller.