On the discrete Wigner function for SU(N)

• Autor(a) principal: Marchiolli, Marcelo A.
• Data de Publicação: 2019
• Outros Autores: Galetti, Diogenes [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1088/1751-8121/ab3bab; http://hdl.handle.net/11449/196177
• topic: discrete Wigner function; group SU(N); finite-dimensional discrete phase spaces; Schwinger unitary operators

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 SU(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 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.