Conclusive discrimination among N equidistant pure states

L. Roa, A.B. Klimov and Carla Hermann Avigliano


We find the allowed complex overlaps for N equidistant pure quantum states. The accessible overlaps define a petal-shaped area on the Argand plane. Each point inside the petal represents a set of N linearly independent pure states and each point on its contour represents a set of N linearly dependent pure states. We find the optimal probabilities of success of discriminating unambiguously in which of the N equidistant states the system is. We show that the phase of the involved overlap plays an important role in the probability of success. For a fixed overlap modulus, the success probability is highest for the set of states with an overlap with phase equal to zero. In this case, if the process fails, then the information about the prepared state is lost. For states with a phase different from zero, the information could be obtained with an error-minimizing measurement protocol.