The ability to uniquely identify a quantum state is integral to quantum science, but for nonorthogonal states, quantum mechanics precludes deterministic, error-free discrimination. However, using the nondeterministic protocol of unambiguous state discrimination enables the error-free differentiation of states, at the cost of a lower frequency of success. We discriminate experimentally between nonorthogonal, 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 1 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.

• Received 14 March 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.020501

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© 2014 Published by American Physical Society