Maximum Confidence Quantum Measurements
  We consider the problem of discriminating between states of a specified set with maximum confidence. For a set of linearly independent states unambiguous discrimination is possible if we allow for the possibility of an inconclusive result. For linearly dependent sets an analogous measurement is one which allows us to be as confident as possible that when a given state is identified on the basis of the measurement result, it is indeed the correct state. 
Sarah Croke, Erika Andersson, Stephen M. Barnett, Claire R. Gilson and   John Jeffers