  We consider the transformations of quantum states obtainable by a process of
the following sort. Combine the given input state with a specially prepared
initial state of an auxiliary system. Apply a unitary transformation to the
combined system. Measure the state of the auxiliary subsystem. If (and only if)
it is in a specified final state, consider the process successful, and take the
resulting state of the original (principal) system as the result of the
process.
  We review known information about exact realization of transformations by
such a process. Then we present results about approximate realization of finite
partial transformations. We consider primarily the issue of approximation to
within a specified positive epsilon, but we also address the question of
arbitrarily close approximation.
