Geometric approach to the discrete Wigner function

Abstract

We analyze the Wigner function constructed on the basis of the discrete rotation and displacement operators labeled with elements of the underlying finite field. We separately discuss the case of odd and even characteristics and analyze the algebraic origin of the non uniqueness of the representation of the Wigner function. Explicit expressions for the Wigner kernel are given in both cases.

25 p. Extended version de short course given in School on Quantum Optics and Quantum Information, November 21-25, 2005, Las trancas, Chillan, Chile