A unified approach to quantum dynamical maps and gaussian Wigner distributions

The KLM conditions are conditions that are necessary and sufficient for a phase-space function to be a Wigner distribution function (WDF). We apply them here to discuss three questions that have arisen recently: (1) For which WDFs P0 will the map P→P0*P be a quantum dynamical map - i.e. a map that takes WDFs to WDFs? (2) What are necessary and sufficient conditions for a phase-space gaussian to be a WDF? (3) Are there non-gaussian, non-negative WDFs? © 1988