Quantum key distribution with vacuum-one-photon entangled states

We present a scheme to realize a quantum key distribution using vacuum-one-photon entangled states created both from Alice and Bob. The protocol consists of an exchange of spatial modes between Alice and Bob and in a recombination which allows one of them to reconstruct the bit encoded by the counterpart in the phase of the entangled state. The security of the scheme is analyzed against some simple kind of attack. The model is shown to reach higher efficiency with respect to prior schemes using phase encoding methods