  The linearity of quantum operations puts many fundamental constraints on the
information processing tasks we can achieve on a quantum system whose state is
not exactly known, just as we observe in quantum cloning and quantum
discrimination. In this paper we show that in probabilistic manner, linearity
is in fact the only one that restricts the physically realizable tasks. To be
specific, if a system is prepared in a state secretly chosen from a linearly
independent pure state set, then any quantum state separation can be physically
realized with a positive probability. Furthermore, we derive a lower bound on
the average failure probability of any quantum state separation.
