Impact of SNR Mismatch on Induced BSCs in CV-QKD Systems Quantized with Arithmetic Reconciliation

Arithmetic Reconciliation (AR) is a recently proposed reconciliation protocol for Continuous-Variable Quantum Key Distribution (CV-QKD) systems operating in low-SNR regimes. Since the channel signal-to-noise ratio (SNR) directly affects the statistical characterization of the induced binary subchannels, inaccuracies in SNR estimation may significantly impact reconciliation performance. In this work, we investigate the effects of SNR mismatch on the Kullback-Leibler (KL) distance, Bit Error Rate (BER), capacities of the BSC subchannels induced by AR quantization and the secret key rate provided by the protocol. The obtained results show that the most significant subchannels are considerably more sensitive to mismatch conditions, especially at moderate and high SNR values. Furthermore, SNR underestimation leads to the selection of excessively robust low-rate error-correcting codes, increasing computational complexity and reducing spectral efficiency, whereas SNR overestimation degrades the effective decoding performance due to insufficient redundancy. These results demonstrate the importance of accurate SNR estimation for reliable and efficient practical implementations of CV-QKD systems employing AR.