# Note about Passive Continuous Variable Quantum Key Distribution over Turbulent Atmospheric Channel

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## Abstract

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## 1. Introduction

## 2. Literature Reviews

## 3. Passive CVQKD Embedded with an AO Unit

## 4. Turbulence Bubble-Modeled Atmospheric Channel

## 5. Performance Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**CVQKD protocol with active state preparation. QM is a quantum memory device which is used to store the outputs from Eve; HERM denotes the high extinction ratio modulator; TRNG denotes true random number generator; ${\omega}_{1}$ is the variance of thermal noise; and ${E}_{1}$ is ancillary modes.

**Figure 2.**CVQKD protocol with passive state preparation. TS is the thermal source; BS denotes the beam splitter; HD means homodyne detector; Att is optical attenuator; and ${\eta}_{\mathrm{D}}$ is the transmittance of the beam splitter.

**Figure 3.**(

**a**) The AO-based CVQKD system in the atmospheric channel. (

**b**) The phase diagram in the atmospheric channel. (

**c**) Schematic diagram of Alice’s preparation setup. (

**d**) Bob’s detection detection setup. BS: beam splitter. PBS: polarization beam splitter. AM: amplitude modulator. VA: voltage attenuator. PM: phase modulator. WFS: wavefront sensor. RTC: real-time controller. DM: deformable mirror. PIN: PIN photodiode.

**Figure 4.**The effect of the proposed AO unit on the transmitted quantum signals in THz band over turbulent atmospheric channel. (

**a**) The waveform of the original Gaussian-distributed signal in time domain. (

**b**) The waveform of signal mixed with Gaussian-distributed noise in time domain. (

**c**) The processed waveform of signal mixed with Gaussian-distributed noise after AO unit in time domain. (

**d**) The signal error of the processed signal.

**Figure 5.**Diagram of the bubble-based atmospheric turbulence channel. (

**a**) Continuous refraction of photon over atmospheric turbulence channel. (

**b**) The transmittance ratio as a function of incident angle ${\theta}_{1}$.

**Figure 6.**The receiver noise ${\xi}_{ex}$ as a function of the transmission distance and the modulation variance.

**Figure 7.**The effect of the refractive index ${n}_{2}$ on performance of the FS CVQKD in the terahertz band over turbulence bubbles.

**Figure 8.**(

**a**) The performance of the AO-based CVQKD system. (

**b**) The total noise ${\chi}_{tot}$ consists of the channel-added noise ${\chi}_{line}$, the AO-added noise ${\chi}_{w}$ and the detection-added noise ${\chi}_{h}$. The parameter ${\chi}_{line}$ is related to the electrical noise ${\u03f5}_{el}$ and transmission T.

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**MDPI and ACS Style**

Mao, Y.; Zhu, Y.; Wang, Y.; Guo, Y.
Note about Passive Continuous Variable Quantum Key Distribution over Turbulent Atmospheric Channel. *Symmetry* **2022**, *14*, 2128.
https://doi.org/10.3390/sym14102128

**AMA Style**

Mao Y, Zhu Y, Wang Y, Guo Y.
Note about Passive Continuous Variable Quantum Key Distribution over Turbulent Atmospheric Channel. *Symmetry*. 2022; 14(10):2128.
https://doi.org/10.3390/sym14102128

**Chicago/Turabian Style**

Mao, Yun, Yiwu Zhu, Yijun Wang, and Ying Guo.
2022. "Note about Passive Continuous Variable Quantum Key Distribution over Turbulent Atmospheric Channel" *Symmetry* 14, no. 10: 2128.
https://doi.org/10.3390/sym14102128