Bases for spin systems and qudits from angular momentum theory
Maurice R. Kibler (IPNL)
TL;DR
This paper constructs spin bases for quantum systems with cyclic symmetry using angular momentum theory, linking them to generalized Pauli matrices, and provides multiple examples for dimensions 2, 3, and 4.
Contribution
It introduces a method to derive spin bases from angular momentum theory, connecting them to generalized Pauli matrices for quantum systems.
Findings
Constructed spin bases for dimensions 2, 3, and 4.
Connected spin bases to generalized Pauli matrices.
Provided explicit examples illustrating the construction.
Abstract
Spin bases of relevance for quantum systems with cyclic symmetry as well as for quantum information and quantum computation are constructed from the theory of angular momentum. This approach is connected to the use of generalized Pauli matrices (in dimension d) arising from a polar decomposition of the group SU(2). Numerous examples are given for d=2, 3 and 4.
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