Multi-Stage CD-Kennedy Receiver for QPSK Modulated CV-QKD in Turbulent Channels

Continuous variable-quantum key distribution (CV-QKD) protocols attract increasing attentions in recent years because they enjoy high secret key rate (SKR) and good compatibility with existing optical communication infrastructure. Classical coherent receivers are widely employed in coherent states based CV-QKD protocols, whose detection performance is bounded by the standard quantum limit (SQL). Recently, quantum receivers based on displacement operators are experimentally demonstrated with detection performance outperforming the SQL in various practical conditions. However, potential applications of quantum receivers in CV-QKD protocols under turbulent channels are still not well explored, while practical CV-QKD protocols must survive from the atmospheric turbulence in satellite-to-ground optical communication links. In this paper, we consider the possibility of using a quantum receiver called multi-stage CD-Kennedy receiver to enhance the SKR performance of a quadrature phase shift keying (QPSK) modulated CV-QKD protocol in turbulent channels. We first derive the error probability of the multi-stage CD-Kennedy receiver for detecting QPSK signals in turbulent channels and further propose three types of multi-stage CD-Kennedy receiver with different displacement choices, i.e., the Type-I, Type-II, and Type-III receivers. Then we derive the SKR of a QPSK modulated CV-QKD protocol using the multi-stage CD-Kennedy receiver and post-selection strategy in turbulent channels. Numerical results show that the multi-stage CD-Kennedy receiver can outperform the classical coherent receiver in turbulent channels in terms of both error probability and SKR performance and the Type-II receiver can tolerate worse channel conditions compared with Type-I and Type-III receivers in terms of error probability performance.