Experimental demonstration of a Hadamard gate for coherent state qubits

We discuss and make an experimental test of a probabilistic Hadamard gate for coherent state qubits. The scheme is based on linear optical components, nonclassical resources, and the joint projective action of a photon counter and a homodyne detector. We experimentally characterize the gate for the coherent states of the computational basis by full tomographic reconstruction of the transformed output states. Based on the parameters of the experiment, we simulate the fidelity for all coherent state qubits on the Bloch sphere.