| Discrimination of quantum states is a challenging problem in quantum physics. If the quantum states are nonorthogonal, they can not be discriminated with unit success probability. Optimum unambiguous discrimination means to have the minimum probability of getting inconclusive result. We study the general POVM formulism to derive a necessary condition of optimum unambiguous discrimination. We also provide an optical implementation of any desired unambiguous discrimination. We show that nonorthogonal quantum states, each realized as a photon split among several modes, can be conditionally distinguished by means of a linear optical network. It is discussed in detail on how to discriminate two and three nonorthogonal quantum states. We have given explicit examples together with the optical networks, which give the maximum success probabilities for several sets of states. We also consider the problem of unambiguous discrimination between subsets. We consider the simplest instance of this problem, the situation in which we are trying to discriminate between a set containing one quantum state and another containing two. A method for finding the optimal strategy for discriminating between these two sets is presented, and analytical solutions for particular cases are given. Finally, we also study the problem of state comparison, and present the analytical solution of optimum unambiguous comparison of two quantum systems, where each of them could be in one of the two known quantum states. |
