Unambiguous discrimination between linearly dependent states with multiplecopies - art. no. 062305

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.