The quantum state discrimination problem is ubiquitous in quantum information and serves as the foundation for many quantum communication schemes proposed so far. This paper investigates the optimal discrimination of three symmetric quantum states with equal prior probabilities. To obtain completely accessible information about the input pure states, this strategy makes improvements to the two standard strategies of quantum state discrimination, namely the minimum error discrimination and unambiguous discrimination. The new discrimination strategy proposed in this paper can be applied to both linearly independent and dependent quantum states.
We propose an experimental setup for discriminating four linearly independent nonorthogonal symmetric quantum states. The setup is based on linear optics only and can be configured to implement both optimal unambiguous state discrimination [Chefles and Barnett, Phys. Lett. A 250, 223 (1998)] and minimum error discrimination. In both cases, the setup is characterized by an optimal success probability. The experimental setup can be generalized to the case of discrimination among
N linearly nonorthogonal symmetric quantum states. We also study the discrimination between two incoherent superpositions of symmetric states. In this case, the setup also achieves an optimal success probability in the case of unambiguous discrimination as well as minimum error discrimination.