  In the theory of classical statistical inference one can derive a simple rule
by which two or more observers may combine {\em independently} obtained states
of knowledge together to form a new state of knowledge, which is the state
which would be possessed by someone having the combined information of both
observers. Moreover, this combined state of knowledge can be found without
reference to the manner in which the respective observers obtained their
information. However, in this note we show that in general this is not possible
for quantum states of knowledge; in order to combine two quantum states of
knowledge to obtain the state resulting from the combined information of both
observers, these observers must also possess information about how their
respective states of knowledge were obtained. Nevertheless, we emphasize this
does not preclude the possibility that a unique, well motivated rule for
combining quantum states of knowledge without reference to a measurement
history could be found. We examine both the direct quantum analogue of the
classical problem, and that of quantum state-estimation, which corresponds to a
variant in which the observers share a specific kind of prior information.
