  We discuss the following variant of the standard minimum error state
discrimination problem: Alice picks the state she sends to Bob among one of
several disjoint state ensembles, and she communicates him the chosen ensemble
only at a later time. Two different scenarios then arise: either Bob is allowed
to arrange his measurement set-up after Alice has announced him the chosen
ensemble, or he is forced to perform the measurement before of Alice's
announcement. In the latter case, he can only post-process his measurement
outcome when Alice's extra information becomes available. We compare the
optimal guessing probabilities in the two scenarios, and we prove that they are
the same if and only if there exist compatible optimal measurements for all of
Alice's state ensembles. When this is the case, post-processing any of the
corresponding joint measurements is Bob's optimal strategy in the
post-measurement information scenario. Furthermore, we establish a connection
between discrimination with post-measurement information and the standard state
discrimination. By means of this connection and exploiting the presence of
symmetries, we are able to compute the various guessing probabilities in many
concrete examples.
