  In the quantum-Bayesian approach to quantum foundations, a quantum state is
viewed as an expression of an agent's personalist Bayesian degrees of belief,
or probabilities, concerning the results of measurements. These probabilities
obey the usual probability rules as required by Dutch-book coherence, but
quantum mechanics imposes additional constraints upon them. In this paper, we
explore the question of deriving the structure of quantum-state space from a
set of assumptions in the spirit of quantum Bayesianism. The starting point is
the representation of quantum states induced by a symmetric informationally
complete measurement or SIC. In this representation, the Born rule takes the
form of a particularly simple modification of the law of total probability. We
show how to derive key features of quantum-state space from (i) the requirement
that the Born rule arises as a simple modification of the law of total
probability and (ii) a limited number of additional assumptions of a strong
Bayesian flavor.
