Direct counterfactual quantum communication protocol beyond single photon source

The direct counterfactual quantum communication protocol involving double chained Mach-Zehnder interferometers requires a single photon input. Here, we show that even with multiphoton light sources, including a strong coherent light source as inputs, the counterfactual communication can be achieved with success probability approaching unity in the ideal asymptotic limit. The path evolution of multiple photons is non-locally controlled. Thus, information is transmitted without any photons, or any other auxiliary information carriers, appearing in the public transmission channel. The effect is quantum since quantum measurements are essential requirement for this protocol. Furthermore, a modified scheme is proposed in which number of interferometers is reduced.