A set of quantum states can be unambiguously discriminated if and only if t
hey are linearly independent. However, for a linearly dependent set, if C c
opies of the state are available, then the resulting C particle states may
form a linearly independent set, and be amenable to unambiguous discriminat
ion. We obtain one necessary and one sufficient condition for the possibili
ty of unambiguous discrimination among N states given that C copies are ava
ilable and that the single copies span a D-dimensional space, These conditi
ons are found to be identical for qubits. We then examine in detail the lin
early dependent trine ensemble. The set of C > 1 copies of each state is a
set of linearly independent lifted trine states. The maximum unambiguous di
scrimination probability is evaluated for all C > 1 with equal a priori pro
babilities.