  We study measurements of the unitary generalization of Pauli operators.
First, an analytical (constructive) solution to the eigenproblem of these
operators is presented. Next, in the case of two subsystems, the Schmidt form
of the eigenvectors is derived to identify measurements which are easy to
implement. These results are utilized to show that quantum cryptography with
two bases, when operating on a two-component qudit, can be realized with
measurements on individual subsystems, assisted with classical communication.
We also discuss feasible devices which perform tomography of polarisation-path
qudits.

Quantum Physics