DISCRETE WIGNER FUNCTION FOR FINITE-DIMENSIONAL SYSTEMS

A phase-space approach to finite-dimensional systems is developed from basic principles. For a system describable by a Hilbert space of dime nsion d we define a one-to-one correspondence between operators and fu nctions on a discrete and finite phase space with d(2) points valid fo r any dimension d. The properties fulfilled by this correspondence and its uniqueness are examined. This formalism is applied to the number difference and phase difference of a two-mode field. This case is comp ared with the marginal distribution for these variables arising from a two-mode Wigner function for number and phase.