Unambiguous discrimination between two rank-2 mixed quantum states

In this paper we consider the problem of the optimal quantum unambiguous detection between two mixed quantum states. More specifically, we consider two mixed quantum states of rank 2 which lie in a Hilbert space of dimension 4. Using duality theory we explicitly characterize the optimal measurement operators. Furthermore, as a by-product of our framework we obtain a closed form solution of unambiguous discrimination between a pure and a mixed quantum state.