Optimum unambiguous discrimination between subsets of nonorthogonal quantum states

It is known that unambiguous discrimination among nonorthogonal 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 nonorthogonal states, $\{|{\psi }_1〉,|{\psi }_2〉,|{\psi }_3〉\},$ we show that the optimal strategy to distinguish $|{\psi }_1〉$ from the set $\{|{\psi }_2〉,|{\psi }_3〉\}$ 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 (multiport) which provide an optical implementation of the optimal strategy.