Parametrized discrete phase-space functions

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Abstract
Using discrete displacement-operator expansion, s-parametrized phase-space functions associated with the operators in a finite-dimensional Hilbert space are introduced and their properties are studied. In particular, the phase-space functions associated with the density operator can be regarded as quasidistributions whose properties are similar to those of the well-known quasidistributions in the continuous phase space. So the Q function (s=-1) is non-negative and can be measured directly in particular experiments, whereas the P function (s=1) corresponds to the diagonal form of the density operator in an overcomplete basis. Except for the W function (s=0), the introduction of discrete phase-space functions requires the choice of a special reference state. We finally present a simple model for measuring the discrete Q function. © 1996 The American Physical Society.

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