A Wigner-function formulation of finite-state quantum mechanics

William K. Wootters

Francis D. Delloro, Job A. Nable

In this work, the version of Wigner transforms and Wigner functions on discrete systems are formulated. Using frame quantization, the star-product of phase space functions are also computed for a particular finite group. Specifically, the Wigner transform, Wigner function and star-product are computed for the dicyclic group Dien. Frames are the discrete version of coherent states. In the literature, quasiprobability distributions are essential in the study of the phase space representations of quantum mechanics, and are naturally associated to frame quantizations. For this work, the unitary irreducible representations of a finite group play an essential role in the construction.

Valerian I. Tatarskii

D. Lalović, Dragomir M Davidović, N. Bijedić

O Cohendet, Ph. Combe, M. Sirugue-Collin

The authors consider a quantum system with a finite number N of states and show that a Markov process evolving in an 'extended' discrete phase space can be associated with the discrete Wigner function of the system. This Wigner function is built using the Weyl quantisation procedure on the group Z N *Z N . Moreover, the authors can use this process to compute the quantum mean values as probabilistic expectations of functions of this process. This probabilistic formulation can be seen as a stochastic mechanics in phase space.

Abner Shimony