Hybrid quantum key distribution using coherent states and photon-number-resolving detectors

We put forward a hybrid quantum key distribution protocol based on coherent states, Gaussian modulation, and photon-number-resolving (PNR) detectors, and show that it may enhance the secret key generation rate (KGR) compared to homodyne-based schemes. Improvement in the KGR may be traced back to the dependence of the two-dimensional discrete output variable on both the input quadratures, thus overcoming the limitations of the original protocol. When reverse reconciliation is considered, the scheme based on PNR detectors outperforms the homodyne one both for individual and collective attacks. In the presence of direct reconciliation, the PNR strategy is still the best one against individual attacks, but for the collective ones the homodyne-based scheme is still to be preferred as the channel transmissivity decreases.