Retrodictively optimal localizations in phase space

In a previous paper it was shown that the distribution of measured values for a retrodictively optimal simultaneous measurement of position and momentum is always given by the initial state Husimi function. This result is now generalized to retrodictively optimal simultaneous measurements of an arbitrary pair of rotated quadratures ◯ θ 1 and [pcirc] θ 2 . It is shown, that given any such measurement, it is possible to find another such measurement, informationally equivalent to the first, for which the axes defined by the two quadratures are perpendicular. It is further shown that the distribution of measured values for such a measurement belongs to the class of generalized Husimi functions most recently discussed by Wünsche and Büzek. The class consists of the subset of Wódkiewicz's operational probability distributions for which the filter reference state is a squeezed vacuum state.