Enhanced secret-key generation from atmospheric optical channels with the use of random modulation: erratum

Chunyi Chen; Chunyi Chen; Qiong Li; Qiong Li

doi:10.1364/OE.482831

Abstract

An erratum is given to correct two typos of Eq. (28) in [Opt. Express 30(25), 45862 (2022) [CrossRef] ]. The corrections do not impact on the results and conclusions of the original article.

Erratum

We recognized two typos in Eq. (28) of [1]; i.e. the two exponents following the two right square brackets therein should be 1/2, instead of −1/2. The correct form of Eq. (28) of [1] should be

(1)$$\begin{array}{c} {\chi _{CE,X}} = {[(\sigma _{x,B}^2 + 1)(\sigma _{x,A}^2 + 1)(\sigma _h^2 + 1) - 1 + (\sigma _{x,X}^2 + 1)\gamma _X^{ - 1}]^{1/2}}\\ \times {[(\sigma _{x,A}^2 + 1)(\sigma _{x,B}^2 + 1)(\sigma _{h,AE}^2 + 1) - 1]^{1/2}} \end{array}$$

The meanings of the quantities $\sigma _{x,A}^2$, $\sigma _{x,B}^2$, $\sigma _h^2$, $\sigma _{x,X}^2$, ${\gamma _X}$ and $\sigma _{h,AE}^2$ are described in [1]. Here we apologize for the typos and stress that none of the results and conclusions presented in [1] are impacted by them.

Funding

Natural Science Foundation of Chongqing (cstc2021jcyj-msxmX0457); National Natural Science Foundation of China (61775022, 62275033).

Disclosures

The authors declare no conflicts of interest.

References

1. C. Chen and Q. Li, “Enhanced secret-key generation from atmospheric optical channels with the use of random modulation,” Opt. Express 30(25), 45862–45882 (2022). [CrossRef]

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Equations (1)

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\begin{matrix} χ_{C E, X} = [(σ_{x, B}^{2} + 1) (σ_{x, A}^{2} + 1) (σ_{h}^{2} + 1) - 1 + (σ_{x, X}^{2} + 1) γ_{X}^{- 1}]^{1 / 2} \\ \times [(σ_{x, A}^{2} + 1) (σ_{x, B}^{2} + 1) (σ_{h, A E}^{2} + 1) - 1]^{1 / 2} \end{matrix}