Optimal unambiguous discrimination between subsets of non-orthogonal quantum states

It is known that unambiguous discrimination among non-orthogonal but linearly independent quantum states is possible with a certain probability of success. Here, we consider a variant of that problem. Instead of discriminating among all of the different states, we shall only discriminate between two subsets of them. In particular, for the case of three non-orthogonal states, we show that the optimal strategy to distinguish between a set containing one of the states from the set containing the other two has a higher success rate than if we wish to discriminate among all three states. Somewhat surprisingly, for unambiguous discrimination the subsets need not be linearly independent. A fully analytical solution is presented, and we also show how to construct generalized interferometers (multiports) that provide an optical implementation of the optimal strategy.