Optimizing state-discrimination receivers for continuous-variable quantum key distribution over a wiretap channel

We address a continuous-variable quantum key distribution protocol employing quaternary phase-shift-keying of coherent states and a non-Gaussian measurement inspired by quantum receivers minimizing the error probability in a quantum-state-discrimination scenario. We consider a pure-loss quantum wiretap channel, in which a possible eavesdropper is limited to collect the sole channel losses. We perform a characterization of state-discrimination receivers and design an optimized receiver maximizing the asymptotic secure key rate (SKR), namely the key-rate optimized receiver (KOR), comparing its performance with respect to the pretty good measurement and the heterodyne-based protocol. We show that the KOR increases the SKR for metropolitan-network distances. Finally, we also investigate the implementations of feasible schemes, such as the displacement feed-forward receiver, obtaining an increase in the SKR in particular regimes.