# Vulnerability of Satellite Quantum Key Distribution to Disruption from Ground-Based Lasers

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Satellite Architecture

#### 2.2. Satellite Optical Scattering Model

#### 2.3. Orbital Dynamics

#### 2.4. Free-Space Link Loss

#### 2.5. Impact on Quantum Bit Error Rate

## 3. Results

#### 3.1. Satellite Optical Scattering Profile

^{2}) and albedo (0.3) of Micius given in Table 1, we are able to estimate the optical scattering cross section of a Micius-type satellite as

#### 3.2. Orbital Dynamics and Visibility

#### 3.3. Excess Photon Rate

^{−2/3}) because these are the conditions under which Micius is currently capable of operating, and are the conditions under which many future QKD satellites will need to work and will achieve their highest quantum key rate.

^{−2/3}reduces the excess photon rate at the ground station by about 60%. While this would significantly decrease the number of excess photons (or require a 3-fold increase in laser power to maintain the same received photon rate), the increased atmospheric turbulence will also significantly increase the losses on the QKD transmission, reducing the achieved quantum key rate, meaning fewer photons from the mobile laser terminal will be required to achieve complete disruption. (It should be noted that, over the 100 km and 1000 km distances involved in these calculations, it cannot be assumed that weather conditions are the same or comparable for ground station and laser terminal).

#### 3.4. Quantum Bit Error Rate Due to Excess Photons

## 4. Discussion

#### 4.1. Challenges Facing the Laser Terminal

#### 4.2. Countermeasures

#### 4.2.1. Receiver Gating

#### 4.2.2. Spectral Filtering

#### 4.2.3. Improved Sensitivity

#### 4.2.4. Satellite Architecture

#### 4.2.5. Higher Orbits

#### 4.2.6. QKD Protocols

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

SPD | single photon detector |

QBER | quantum bit error rate |

QKD | quantum key distribution |

## References

- Bennet, C.H.; Brassard, G. Quantum cryptography: Public key distribution and coin tossing. In Proceedings of the International Conference on Computers, Systems and Signal Processing, Bangalore, India, 9–12 December 1984; pp. 175–179. [Google Scholar]
- Diamanti, E.; Lo, H.K.; Qi, B.; Yuan, Z. Practical challenges in quantum key distribution. NPJ Quant. Inf.
**2016**, 2, 1–12. [Google Scholar] [CrossRef] [Green Version] - Yin, H.-L.; Chen, T.-Y.; Yu, Z.-W.; Liu, H.; You, L.-X.; Zhou, Y.-H.; Chen, S.-J.; Mao, Y.; Huang, W.-Q.; Zhang, W.-J.; et al. Measurement-device-independent quantum key distribution over a 404 km optical fiber. Phys. Rev. Lett.
**2016**, 117, 190501. [Google Scholar] [CrossRef] [PubMed] - Pittaluga, M.; Minder, M.; Lucamarini, M.; Sanzaro, M.; Woodward, R.I.; Li, M.J.; Yuan, Z.; Shields, A.J. 600-km repeater-like quantum communications with dual-band stabilization. Nat. Phot.
**2021**, 15, 1–6. [Google Scholar] [CrossRef] - Brassard, G.; Lutkenhaus, N.; Mor, T.; Sanders, B.C. Limitations on practical quantum cryptography. Phys. Rev. Lett.
**2000**, 85, 1330–1333. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Zukowski, M.; Zeilinger, A.; Horne, M.A.; Ekert, A.K. Event-ready-detectors: Bell experiment via entanglement swapping. Phys. Rev. Lett.
**1993**, 71, 4287–4290. [Google Scholar] [CrossRef] [PubMed] - Liao, S.K.; Cai, W.Q.; Liu, W.Y.; Zhang, L.; Li, Y.; Ren, J.; Pan, J.W.; Yin, J.; Shen, Q.; Cao, Y.; et al. Satellite-to-ground quantum key distribution. Nature
**2017**, 549, 43–47. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Bedington, R.; Arrazola, J.M.; Ling, A. Progress in satellite quantum key distribution. Quant. Inf.
**2017**, 3, 1–3. [Google Scholar] [CrossRef] - Lo, H.-K.; Ma, X.; Chen, K. Decoy state quantum key distribution. Phys. Rev. Lett.
**2005**, 94, 230504. [Google Scholar] [CrossRef] [Green Version] - Degnan, J.J. Millimeter accuracy satellite laser ranging: A review. In Contributions of Space Geodesy to Geodynamics: Technology; Smith, D.E., Turcotte, D.L., Eds.; American Geophysical Union: Washington, DC, USA, 1993; pp. 133–162. [Google Scholar]
- Andrews, L.C.; Phillips, R.L. Laser Beam Propagation through Random Media, 2nd ed.; SPIE: Bellingham, WA, USA, 2005; pp. 481–492. [Google Scholar]
- Shor, P.W.; Preskill, J. Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett.
**2000**, 85, 441. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Biham, E.; Boyer, M.; Boykin, P.O.; Mor, T.; Roychowdhury, V. A proof of the security of quantum key distribution. J. Cryptol.
**2006**, 19, 381. [Google Scholar] [CrossRef] [Green Version] - Mayers, D. Unconditional security in quantum cryptography. J. ACM
**2001**, 48, 351–406. [Google Scholar] [CrossRef] - Collins, R.J.; Clarke, P.J.; Fernandez, V.; Gordon, K.J.; Makhonin, M.N.; Timpson, J.A.; Tahraoui, A.; Hopkinson, M.; Fox, A.M.; Skolnick, M.S.; et al. Quantum key distribution system in standard telecommunications fiber using a short wavelength single photon source. J. App. Phys.
**2010**, 107, 073102. [Google Scholar] [CrossRef] [Green Version] - Mailloux, L.O.; Engle, R.D.; Grimaila, M.R.; Hodson, D.D.; Colombi, J.M.; McLaughlin, C.V. Modeling decoy state Quantum Key Distribution systems. J. Def. Model. Sim.
**2015**, 12, 489–506. [Google Scholar] [CrossRef] - Er-long, M.; Zheng-fu, H.; Shun-sheng, G.; Tao, Z.; Da-Sheng, D.; Guang-Can, G. Background noise of satellite-to-ground quantum key distribution. New J. Phys.
**2005**, 7, 215. [Google Scholar] [CrossRef] - Steindorfer, M.A.; Kirchner, G.; Koidl, F.; Wang, P.; Jilete, B.; Flohrer, T. Daylight space debris laser ranging. Nat. Comm.
**2020**, 11, 1–6. [Google Scholar] [CrossRef] [PubMed] - Ekert, A.K. Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett.
**1991**, 67, 661. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Grosshans, F.; Grangier, P. CV quantum cryptography using coherent states. Phys. Rev. Lett.
**2002**, 88, 057902. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Braunstein, S.L.; Van Loock, P. Quantum information with continuous variables. J. Rev. Mod. Phys.
**2005**, 77, 513. [Google Scholar] [CrossRef] [Green Version] - Dequal, D.; Vidarte, L.T.; Rodriguez, V.R.; Vallone, G.; Villoresi, P.; Leverrier, A.; Diamanti, E. Feasibility of satellite-to-ground continuous-variable quantum key distribution. NPJ Quant. Inf.
**2021**, 7, 1–10. [Google Scholar] [CrossRef] - Kirchner, G.; Koidl, F.; Ploner, M.; Lauber, P.; Utzinger, J.; Schreiber, U.; Eckl, J.; Wilkinson, M.; Sherwood, R.; Giessen, A.; et al. Multistatic laser ranging to space debris. In Proceedings of the 18th International Workshop on Laser Ranging, Fujiyoshida, Japan, 11–15 November 2013; pp. 1–9. [Google Scholar]

**Figure 1.**Simplified schematic of the setup to determine the optical scattering profile of a wrinkled gold foil target. Setup (

**a**) simulates the scenario where light from the laser terminal scatters from the satellite and is detected by the QKD ground station, while setup (

**b**) simulates the scenario where light from the laser terminal is detected by a satellite-based QKD receiver due to photons entering the receiving optic highly off-axis and scattering internally. SPD, single photon detector; SMF, single-mode fiber; MMF, multi-mode fiber.

**Figure 2.**Contour plot showing the areas in which different fractions of the QKD transmission window are visible to the laser terminal. The black dot represents the QKD ground station, and the black bar represents the QKD transmission window.

**Figure 3.**QKD transmission window coverage for laser terminals (

**a**) 100 km away and (

**b**) 1000 km away from the QKD ground station. The black dot represents the QKD ground station, and the black bar represents the QKD transmission window. The red dot represents an example location for the laser terminal, and the red bar shows the portion of the QKD transmission window that the satellite is visible to the laser terminal from this location.

**Figure 4.**Excess photon rate at the QKD ground station and optical power loss over time (represented in seconds elapsed since the satellite came into view of the ground station) achieved for a 1 kW laser launched via a 10 cm telescope 100 km from the QKD ground.

**Figure 5.**Excess photon rate at the QKD ground station and optical power loss over time (represented in seconds elapsed since the satellite came into view of the ground station) achieved for a 1 kW laser launched via a 30 cm telescope 1000 km from the ground station. (The satellite moves out of view of the laser terminal around 220 s assuming a lower elevation limit of 10°).

**Figure 6.**Additional QBER due to laser terminal with 10 cm optic from 100 km distance with 1 kW laser power. Green trace, detected QKD signal photon rate; blue trace, detected excess noise photon rate; red trace, additional QBER due to excess noise photons; dashed red line, QBER limit at which no secure key can be generated.

**Figure 7.**Additional QBER due to laser terminal with 10 cm optic from 1000 km distance with 1 kW laser power. Green trace, detected QKD signal photon rate; blue trace, detected excess noise photon rate; red trace, additional QBER due to excess noise photons; dashed red line, QBER limit at which no secure key can be generated.

**Figure 8.**Additional QBER generated from two symmetrically placed 1 kW laser terminals both 1000 km from the receiving station so that one overlaps the early and the other the late part of the transmission window. At no point during the transmission window from the Satellite is any secure key generated as the additional QBER always exceeds 11%. Green trace, detected QKD signal photon rate; blue trace, detected excess noise photon rate; red trace, additional QBER due to excess noise photons; dashed red line, QBER limit at which no secure key can be generated.

Parameter | Satellite Design |
---|---|

Orbit | Sun-synchronous circular orbit at 500 km altitude, 7.6 km/s. Satellite visible to ground station from elevations of approximately 15° to 10°. |

Satellite bus | Approximately 2 m × 2 m, coated in metallized polymer thermal shielding with an albedo of approximately 0.3. |

Satellite attitude | Coarse pointing — satellite is bodily oriented towards ground station with 0.5° precision. |

Satellite QKD transmitter optic | 300 mm aperture Cassegrain telescope. 10 $\mathsf{\mu}$rad divergence, 22 dB diffraction loss at 1200 km. |

Ground station QKD receiver optic | 1 m aperture Ritchey-Chretien telescope. Approximately 16% optical efficiency from aperture to QKD receiver system. |

QKD wavelength | 848.6 nm |

QKD protocol | Decoy-state BB84 [9] with three intensity levels. |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gozzard, D.R.; Walsh, S.; Weinhold, T.
Vulnerability of Satellite Quantum Key Distribution to Disruption from Ground-Based Lasers. *Sensors* **2021**, *21*, 7904.
https://doi.org/10.3390/s21237904

**AMA Style**

Gozzard DR, Walsh S, Weinhold T.
Vulnerability of Satellite Quantum Key Distribution to Disruption from Ground-Based Lasers. *Sensors*. 2021; 21(23):7904.
https://doi.org/10.3390/s21237904

**Chicago/Turabian Style**

Gozzard, David R., Shane Walsh, and Till Weinhold.
2021. "Vulnerability of Satellite Quantum Key Distribution to Disruption from Ground-Based Lasers" *Sensors* 21, no. 23: 7904.
https://doi.org/10.3390/s21237904