  In approaches to quantum theory in which the quantum state is regarded as a
representation of knowledge, information, or belief, two agents can assign
different states to the same quantum system. This raises two questions: when
are such state assignments compatible? and how should the state assignments of
different agents be reconciled? In this paper, we address these questions from
the perspective of the recently developed conditional states formalism for
quantum theory [arXiv:1107.5849]. Specifically, we derive a compatibility
criterion proposed by Brun, Finkelstein and Mermin from the requirement that,
upon acquiring data, agents should update their states using a quantum
generalization of Bayesian conditioning. We provide two alternative arguments
for this criterion, based on the objective and subjective Bayesian
interpretations of probability theory. We then apply the same methodology to
the problem of quantum state improvement, i.e. how to update your state when
you learn someone else's state assignment, and to quantum state pooling, i.e.
how to combine the state assignments of several agents into a single assignment
that accurately represents the views of the group. In particular, we derive a
pooling rule previously proposed by Spekkens and Wiseman under much weaker
assumptions than those made in the original derivation. All of our results
apply to a much broader class of experimental scenarios than have been
considered previously in this context.
