In continuous-variable quantum key distribution, information reconciliation is required to extract a shared secret key from correlated random variables obtained through the quantum channel. Reverse reconciliation (RR) is generally preferred, since the eavesdropper has less information about Bob’s measurements than about Alice’s transmitted symbols. When discrete modulation formats are employed, however, soft information is available only at Bob’s side, while Alice has access only to hard information (her transmitted sequence). This forces her to rely on hard-decision decoding to recover Bob’s key. In this work, we introduce a novel RR technique for PAM (and QAM) in which Bob discloses a carefully designed soft metric to help Alice recover Bob’s key, while leaking no additional information about the key to an eavesdropper. We assess the performance of the proposed technique in terms of the achievable secret key rate (SKR) and its bounds, showing that the achievable SKR closely approaches the upper bound, with a significant gain over hard-decision RR. Finally, we implement the scheme at the coded level using binary LDPC codes with belief-propagation decoding, assess its bit-error rate through numerical simulations, compare the observed gain with theoretical predictions from the achievable SKR, and discuss the residual gap.

To achieve the maximum information transfer and face a possible eavesdropper, the samples transmitted in continuous-variable quantum key distribution (CV-QKD) protocols are to be drawn from a continuous Gaussian distribution. As a matter of fact, in practical implementations the transmitter has a finite (power) dynamics and the Gaussian sampling can be only approximated. This requires the quantum protocols to operate at small powers. In this paper, we show that a suitable probabilistic amplitude shaping of a finite set of symbols allows to approximate at will the optimal channel capacity also for increasing average powers. We investigate the feasibility of this approach in the framework of CV-QKD, propose a protocol employing discrete quadrature amplitude modulation assisted with probabilistic amplitude shaping, and we perform the key generation rate analysis assuming a wiretap channel and lossless homodyne detection.