In this paper, we study the comparison between two different methods of detection regarding key generation rate in a quantum key distribution system. We illustrate that after a threshold PNR detection outperforms homodyne detection.
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.
What we believe to be a new architecture based on dual-branch photon-number-resolving (DB-PNR) detectors for the receiver in the hybrid quantum key distribution (QKD) is introduced. DB-PNR scheme empowers the receiver to detect both quadratures of the coherent state simultaneously. Our results show that using DB-PNR detectors, the key generation rate (KGR) is almost doubled as compared to homodyne detection which detects only one quadrature at a time. The mutual information is enhanced by around 0.85 bits/symbol using DB-PNR as compared to heterodyne detection. DB-PNR is also found to outperform the heterodyne detection against Eve's individual and collective attacks. PNR-based detection schemes require less local oscillator (LO) power compared to homodyne/heterodyne detection schemes and thereby, the power efficiency of the receiver is enhanced.