Discriminating single-photon states unambiguously in high dimensions

The ability to uniquely identify a quantum state is integral to quantum science, but for non-orthogonal states, quantum mechanics precludes deterministic, error-free discrimination. However, using the non-deterministic protocol of unambiguous state discrimination (USD) enables error-free differentiation of states, at the cost of a lower frequency of success. We discriminate experimentally between non-orthogonal, high-dimensional states encoded in single photons; our results range from dimension $d=2$ to $d=14$. We quantify the performance of our method by comparing the total measured error rate to the theoretical rate predicted by minimum-error state discrimination. For the chosen states, we find a lower error rate by more than one standard deviation for dimensions up to $d=12$. This method will find immediate application in high-dimensional implementations of quantum information protocols, such as quantum cryptography.