  We present a method for computing the action of conditional linear optical
transformations, conditioned on photon counting, for arbitrary signal states.
The method is based on the Q-function, a quasi probability distribution for
anti normally ordered moments. We treat an arbitrary number of signal and
ancilla modes. The ancilla modes are prepared in an arbitrary product number
state. We construct the conditional, non unitary, signal transformations for an
arbitrary photon number count on each of the ancilla modes.
