  The distribution of measured values for maximally accurate, unbiased
simultaneous measurements of position and momentum is investigated. It is
shown, that if the measurement is retrodictively optimal, then the distribution
of results is given by the initial state Husimi function (or Q-representation).
If the measurement is predictively optimal, then the distribution of results is
related to the final state anti-Husimi function (or P-representation). The
significance of this universal property for the interpretation of the Husimi
function is discussed.
