Bases for Spin Systems and Qudits

There is a growing interest these days for the field of quantum information and quantum computation (for which classical bits are replaced by qubits in dimension 2 and qudits in dimension d). This field is at the crossing of mathematics, informatics and quantum physics. In this work, bases of relevance for spin systems with cyclic symmetry as well as for quantum information and quantum computation are discussed from the theory of angular momentum and group-theoretical methods. This approach is connected to the use of generalized Pauli matrices (in dimension d) arising from a polar decomposition of the group SU2. Examples are given for d = 2, 3 and 4.