Transformation of quasi-distributions

Abstract

We derive a general operator transformation between any two functions and we show that the operator transformation of quantum quasi-distributions is a special case. We also show that our approach generalizes the Edgeworth series of standard probability theory, and results in a unified approach for the transformation of probability densities. Our approach generalizes the classical Edgeworth series in two ways. It relates two arbitrary distributions rather than one of them being a Gaussian and secondly we generalize to an arbitrary Hermitian operator rather than the differentiation operator which appears in the Edgeworth formulation. We also consider applying the transformation to the same distribution but at different times.