Quasiprobability methods for multimode conditional optical gates

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.