Non-commutative Bayesian expectation and its connection to quantum theory Available to Purchase

Bayesian probability considers probabilities as degrees of plausibility that must be updated according to newly available information or evidence. In the standard application of this theory, the possible side effects of the act of measurement are not considered, and because of this the results of the updating do not depend on the ordering of two such measurements. In this work we develop the application of Bayesian probability theory to non-commutative measurements on a system. We show that the resulting formalism can be cast in an abstract way which is surprisingly close to quantum theory, together with a complex Hilbert space, linear operators representing measurements and a density operator encoding a state of knowledge.