Sequential discrimination of qudits by multiple observers

We discuss a scheme in which sequential state-discrimination measurements are performed on qudits to determine the quantum state in which they were initially prepared. The qudits belong to a set of nonorthogonal quantum states and hence cannot be distinguished with certainty. Unambiguous state discrimination allows error-free measurements at the expense of occasionally failing to give a conclusive answer about the state of the qudit. Qudits have the potential to carry more information per transmission than qubits. We considered the situation in which Alice sends one of N qudits, where the dimension of the qudits is also N. We look at two cases, one in which the states all have the same overlap and one in which the qudits are divided into two sets, with qudits in different sets having different overlaps. We also study the robustness of our scheme against a simple eavesdropping attack and found that by using qudits rather than qubits, there is a greater probability that an eavesdropper will introduce errors and be detected.