Figure 1. Two-way CV-QKD protocol. Steps: forward, Bob prepares coherent states of amplitude β and density matrix ρ(β) and sends them through the noisy channel.

Using the circuit in ON configuration, Alice applies a random displacement on encoding information in the amplitude α. Backward, Alice then sends the quantum state to Bob who applies heterodyne detection with outcome , and applies classical post-processing to subtract the reference amplitude β to recover α. In OFF configuration, the circuit is opened at Alice’s station. She applies heterodyne detection on the reference state, obtaining the variable α. She then prepares a new coherent state which is sent back to Bob who heterodynes this state obtaining the variable . During the quantum communication Eve, as well as Bob, does not know which setup of the circuit has been adopted. For this reason, she is forced to attack both communication steps, and cannot adapt her attack to the ON/OFF setup.