Bases for spin systems and qudits from angular momentum theory

Spin bases of relevance for quantum systems with cyclic symmetry as well as for quantum information and quantum computation are constructed from angular momentum and Lie algebraic methods. This approach is connected to the use of generalized Pauli matrices (in dimension d) arising from a polar decomposition of the group SU ( 2 ) . Such a decomposition leads to a Weyl pair which can be used as an integrity basis for constructing a generalized Pauli group and the Lie algebra of the unitary group U ( d ) . The case where d is a prime integer yields a maximal set of d + 1 mutually unbiased bases. Numerous examples are given for d = 2 , 3 and 4.