Unambiguous discrimination and exact cloning reduce the square-overlap betw
een quantum states, exemplifying the more general type of procedure we term
state separation. We obtain the maximum probability with which two equipro
bable quantum states can be separated by an arbitrary degree, and find that
the established bounds on the success probabilities for discrimination and
cloning are special cases of this general bound. The latter also gives the
maximum probability of successfully producing N exact copies of a quantum
system whose state is chosen secretly from a known pair, given M initial re
alizations of the state, where N > M. We also discuss the relationship betw
een this bound and that on unambiguous state discrimination.