Atmospheric effects on continuous-variable quantum key distribution

Abstract

Compared to fiber continuous-variable quantum key distribution (CVQKD), atmospheric link offers the possibility of a broader geographical coverage and more flexible transmission. However, there are many negative features of the atmospheric channel that will reduce the achievable secret key rate, such as beam extinction and a variety of turbulence effects. Here we show how these factors affect performance of CVQKD, by considering our newly derived key rate formulas for fading channels, which involves detection imperfections, thus form a transmission model for CVQKD. This model can help evaluate the feasibility of experiment scheme in practical applications. We found that performance deterioration of horizontal link within the boundary layer is primarily caused by transmittance fluctuations (including beam wandering, broadening, deformation, and scintillation), while transmittance change due to pulse broadening under weak turbulence is negligible. Besides, we also found that communication interruptions can also cause a perceptible key rate reduction when the transmission distance is longer, while phase excess noise due to arrival time fluctuations requires new compensation techniques to reduce it to a negligible level. Furthermore, it is found that performing homodyne detection enables longer transmission distances, whereas heterodyne allows higher achievable key rate over short distances. heterodyne detection. Based on the deduced key rate formula, we consider three key parameters that affect the key rate. First, the transmittance change due to beam extinction [21] and turbulence effects (temporal pulse broadening, beam wandering, broadening, deformation, and scintillation) [22] are considered, where extinction likes the attenuation in an optical fiber. Our results demonstrate that beam wandering, broadening and deformation are the main turbulence effects affecting the achievable key rate. Second, we consider the communication interruption caused by angle-of-arrival fluctuations [20], and we found that the interruption probability is noticeable in the case of long-distance transmission. Third, we estimate the excess noise caused by pulse arrival time fluctuations which is found to be quite large. Based on the impacts mentioned above, we conduct a performance analysis.This paper is organized as follows. In section 2, we deduce the achievable secret key rate over the atmospheric channel. In section 3, with the result of section 2, we show how atmospheric effects affect the performance of GMCS CVQKD. In section 4, We consider all the implications mentioned in section 3 and perform a performance analysis. Finally we come to the conclusion and discussion in section 5.

Blind channel estimation for continuous‐variable quantum key distribution

“…Here, we assume that the receiver is approximately as a point receiver and the interruption probability P due to angle of arrival fluctuations is not considered. All variables needed in SKR analysis are consistent with those in References 15 and 23. The parameter‐estimation‐based achievable SKR under atmospheric weak and moderate‐to‐strong turbulence channel are depicted in Figures 4A, 5A and 4B, 5B, respectively.…”

“…Thus, the MSE of BPE and MPE can be respectively calculated as follows where is the estimated channel transmittance, and is the average channel transmittance on the basis of the historical data, approximates to practical channel transmittance. Based on Reference 15, 23, and 24, the statistical analysis of MSE of BPE and MPE is shown in Table 1. Suppose that there exist 10 subchannels with transmittance of T 1 , T 2 ,…, T 10 , respectively, in the atmospheric channel and there are N /10 states transmission in each subchannel.…”

“…In the finite‐size regime, the BPE‐based achievable SKR K B under reconciliation efficiency β R is given as 15,23 where P stands for interruption probability due to angle of arrival fluctuations under considering the high directivity of laser transmission, and N is the total number of variables propagated from Alice to Bob. And Δ( N ) is related to the security of the privacy amplification 24 …”

“…Thus, the mutual information of Alice and Bob can be obtained by, 15,23 …”

“…Since the effect of BPE cannot be evaluated intuitively, we turn to employ the approximate atmospheric channel model described in References 15 and 23 to demonstrate its results. Therefore, the achievable SKR based on parameter estimation with reconciliation efficiency β R can be expressed as 15 where and are the estimated value which can be calculated using Equations () and ().…”