  Is there any point of principle that prohibits us from doing one or more
forms of quantum information processing? It is now well known that an unknown
quantum state can neither be copied nor deleted perfectly. Given a set of
states which are not necessarily orthogonal, is it possible to compare any two
states from the set, given some reasonable ordering of such states? Is it
possible to sort them in some specific order? In the context of quantum
computation, it is shown here that there is no quantum circuit implementing a
unitary transformation, for comparing and sorting an unrestricted set of
quantum states.
