Free-space continuous-variable quantum key distribution in atmospheric channels based on low-density parity-check codes

Free-space continuous-variable quantum key distribution (CV-QKD) links provide greater information capability and broader geographical coverage. A major challenge for the practical use of free-space quantum systems is that the signal-to-noise ratios of the channels are relatively low and are sensitive to atmospheric disturbance. The atmospheric channel has several negative characteristics that diminish the secret key rate, such as beam extinction and various turbulence effects. The effect of beam wandering on the quantum properties is mainly considered, and the probability distribution of the transmission coefficient is derived to establish the channel model. Low-density parity-check (LDPC) codes operated in the reconciliation procedure are utilized to deal with information interactivity. However, the LDPC codes need to be chosen from a range of codes, where the code rate is considered in low signal-to-noise ratio free-space links. The accumulate-repeat-accumulate code is adopted to improve the decoding threshold of a code. It is found that the multi-edge feature of extended codes is beneficial to the performance of short- and medium-length codes. And numerical results show the proposed scheme provides enhancement in the reconciliation efficiency. LDPC codes containing an additional structure that facilitates decoding could be suitable for free-space CV-QKD protocols when weak atmospheric turbulence is considered.