On the discrete Wigner function for SU(N)

Abstract

We present a self-consistent theoretical framework for finite-dimensional discrete phase spaces that leads us to establish a well-grounded mapping scheme between Schwinger unitary operators and generators of the special unitary group $\mathrm{SU}(\mathrm{N})$. This general mathematical construction provides a sound pathway to the formulation of a genuinely discrete Wigner function for arbitrary quantum systems described by finite-dimensional state vector spaces. To illustrate our results, we obtain a general discrete Wigner function for the group $\mathrm{SU}(3)$ and apply this to the study of a particular three-level system. Moreover, we also discuss possible extensions to the discrete Husimi and Glauber-Sudarshan functions, as well as future investigations on multipartite quantum states.

Comments: 22 pages, 6 figures, minor changes