  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.
