Majorana Stars of Odd and Even Coherent States of the Generalized Weyl-Heisenberg Oscillator \(\mathcal{A}_{\kappa }\)

We establish an interesting connection between a generalized variant of the Weyl–Heisenberg algebra and the qudit algebra spanned by the raising and lowering operators of a d-level quantum system. We also discuss the realization of the qudit algebra in terms of the elementary excitation operators of \((d-1)\) identical two-level quantum systems. This construction provides the Fock representation space of the qudit algebra, spanned by Dicke states, as well as the analytical Bargmann realization, which offers a geometrical picture representing each qubit on the Bloch sphere. This approach employs the formalism of coherent states and the concept of Majorana stars. As an illustration, we examine the determination of Majorana stars for even and odd coherent states.