General Bayesian theories and the emergence of the exclusivity principle. (arXiv:1901.11412v2 [quant-ph] UPDATED)

We construct a general Bayesian framework that can be used to organize
beliefs and to update them based on outcomes of experiments. The framework
includes classical and quantum Bayesian inference, as well as other alternative
models of Bayesian reasoning that may arise in future physical theories. It is
only based on the validity of Bayes' rule and the requirement that the agent's
beliefs are consistent across time. From these requirements, we show that the
ideal experiments within every Bayesian theory must satisfy the exclusivity
principle which is a key to explain quantum correlations. A question that is
still open is whether Bayesian reasoning, by itself, is sufficient to recover
all of quantum theory.

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