Conditional sign flip via teleportation

We present a model to realize a probabilistic conditional sign flip gate using only linear optics. The gate operates in the space of number-state qubits and is obtained by a nonconventional use of the teleportation protocol. Both a destructive and a nondestructive version of the gate are presented. In the former case an Hadamard gate on the control qubit is combined with a projective teleportation scheme mixing control and target. The success probability is 1∕2. In the latter case we need a quantum encoder realized via the interaction of the control qubit with an ancillary state composed of two maximally entangled photons. The success probability is 1∕4.