Underwater continuous-variable quantum key distribution with faster-than-Nyquist scheme

The transmission rate of traditional underwater discrete modulation continuous variable quantum key distribution (CV-QKD) scheme is limited by Nyquist criterion. Considering the limitation of Nyquist criterion and the large attenuation coefficient of the seawater channel, it is a challenge to enhance the secret key rate of the traditional underwater discrete modulation CV-QKD without relying on physical hardware. To solve this problem, we propose an underwater discrete modulation CV-QKD with faster-than-Nyquist (FTN) scheme; namely, a FTN signal generator is employed to make the discrete modulated signals obtain FTN rate at the sender’s side. Then an equalizer and a decoder are used to restore the sampled symbols to the original information by taking four typical seawater channels into account. The simulation results show that compared to the traditional Nyquist transmission scheme, the proposed protocol can effectively improve the secret key rate and underwater secure distance no matter what type of water is considered. These results indicate that the proposed scheme can break the constraints of Nyquist criterion, thus achieving a more efficient underwater discrete modulation CV-QKD scheme. Furthermore, we also consider the finite-size effect, which provides more practical results than those achieved in the asymptotic limit.