Majorana stellar representation of phase states of symmetric multi-qubit systems

In this paper, we construct à la Pegg–Barnett the phase states for a qudit ([Formula: see text]-level) system. The corresponding elementary excitation operators are identified with the raising and lowering generators generating a special variant of the generalized Weyl–Heisenberg algebras. The Majorana stellar representation for the phase states of a [Formula: see text]-level quantum system is discussed. In this sense, we employ the coherent states formalism and we use an analytical representation of Fock–Bargmann type to realize the elements of the representation space of the qudit algebra. This leads to coherent states of Perelomov type which provides a geometrical way to visualize a qudit phase state by mean a collection of [Formula: see text] points on the surface of the Bloch sphere.