Simulating Satellite Quantum Communication Channels Máté Galambos1, László Bacsárdi1,2, András Kiss2 1Department
of Networked Systems and Services, Budapest University of Technology and Economics (BME), Hungary 2Institute of Informatics and Economics, University of Sopron, Hungary galambos.mate@gmail.com
Why should we use quantum cannels? • A quantum bit is a unit of information stored in a quantum system (e.g. in an elementary particle) [1] • Quantum bits behave differently than classical bits • One difference: Reading the value of an unknown quantum bit (by copying or measuring) overwrites it [1] → Communicating parties can use this to detect an eavesdropping attempt [1] → Great for cryptography! • Quantum channel length is limited by losses • Free space communication has lower losses than optical cables [2]: ∙ Optical cables can bridge a few hundred km distance ∙ Free space communication can bridge several thousand km
quantum-based satellite communications
Research problem • The atmosphere is a complicated, weather dependent system • Several factors affect optical loss • These factors can change rapidly • The Hamiltonian of air is unknown
Fig.1. Classical beams of light suffer distortions in air. On the top of the figure we see the effect of atmospheric gases (which scatter blue light more, giving the sky its color). A bit lower the mountains are obscured by aerosols (like dust and haze). In the middle of the figure, where the plain meets the mountains we see a mirage (a distortion caused by strong temperature fluctuations). Weaker forms of these temperature dependent distortions are always present in the atmosphere (this is why the stars seem to shimmer).
Solution • Model quantum communication using a quasi-classical approach ∙ Treat the classical beam as a statistics of photons ∙ Use measurement data [3] to calculate gas and aerosol extinction ∙ Use models of classical beam spreading [4][5] to calculate detection probability
Losses 80
Fig.2. Comparison of measured and calculated losses. The solid lines show the reported losses in the QuESS experiment [2] which established two quantum downlinks (one to Lijiang city and another to Delingha). The bars show calculated values—one corresponding to hazy weather, the other to clear weather. These losses consist of multiple parts: shades of blue represent the Satellite-Lijiang channel, while shades of red represent the Satellite-Delingha channel. In each case the reported value of internal system losses, beam spreading/pointing error and atmospheric extinction are taken into account. It’s important to stress that in this figure we relied on the reported value of beam spreading instead of the calculated value.
Satellite-Delingha -- other
70
Satellite-Delingha -- aerosol
60 Loss [dB]
• The model consists of several parts: ∙ Calculating beam spreading ∙ Calculating losses ∙ Taking into account reported system losses • Predictions are checked against experimental data [2] • Most of the predictions agree with measurements ∙ Aerosol extinction, detector and beam profile models are likely accurate
50
Satellite-Delingha -- pointing/spreding
40
Satellite-Lijiang -- other
30
Satellite-Lijiang -- aerosol
20
Satellite-Lijiang -- pointing/spreding
10
Reported value (minimum)
0 Clear weather
Reported value (maximum)
Hazy weather
Open questions Wave Optics Model
12
12
10
10
8
8 Beam spreading s [mrad]
Beam spreading s [mrad]
Geometrical Optics Model
6
6
4
4
2
2
0
0 HV 5/7 Larger telescope (0.3 m diameter)
HV Night Greenwood Smaller telescope (0.18 m diameter)
Reported value
HV 5/7 Larger telescope (0.3 m diameter)
Fig.4. Calculated and measured values of beam spreading. While calculated values are in the same order of magnitude as each other, they are several orders of magnitude smaller than the measured value [2]. Left: results obtained using a geometrical optics based model [4]. Right: results calculated using a wave optics based model [5]. Bars show our calculated results, while a solid black line represents the reported beam spreading. Results are grouped by turbulence model and the models are named on the legends. In the QuESS experiment [2] the satellite was equipped with a larger and a smaller transmitter telescope. White bars correspond to the larger telescope, while black bars correspond to the smaller telescope.
HV Night Greenwood Smaller telescope (0.18 m diameter)
Reported value
Quantum Satellite Communication Simulator
Fig.5. Cover of the Quantum Satellite Communication Simulator 2.0
• Calculated values of beam spreading agree with each other, but not with the experiment [2] • We used two models of beam spreading: ∙ One is based on geometrical optics [4] ∙ The other is based on wave optics [5] • Both models require a turbulence profile as an input • We tried three turbulence profiles, these were: ∙ Greenwood model of turbulence [6] ∙ Hufnagel-Valley model of turbulence [6] ∙ Hufnagel-Valley Night model of turbulence [6] • Calculated values are too small • The reason for this discrepancy is currently unknown
• The aim of the simulation software is to calculate performance characteristics of quantum communication channels. • Development started in 2010 • Handling different orbits and QKD protocols • Available: mcl.hu/quantum/simulator
Our research group at BME • theory of quantum computation and communications • quantum channel coding • quantum error correction • quantum cryptography • quantum repeaters • quantum networks • quantum space communications • developing the first Hungarian CV-QKD device • visualizing multi-qubit systems using fractal representation • undergraduate and graduate courses about quantum computing and communications
References [1] S. Imre, L. Gyongyosi, “Advanced Quantum Communications: An Engineering Approach,” Hoboken, New Jersey, Wiley-IEEE Press, 2012. [2] J. Yin, et al., “Satellite-based entanglement distribution over 1200 kilometers,” Science, vol. 356, iss. 6343, pp.1140-1144. 2017. [3] R.A. McClatchey, et al., “Optical properties of the atmosphere,” (No. AFCRL-72-0497), Air Force Cambridge Research Labs, Hanscom Afb Ma. 1972. [4] J.H. Churnside, R.J. Lataitis, “Wander of an optical beam in the turbulent atmosphere,” Applied Optics, vol. 29, iss. 7, pp. 926-930, 1990. [5] H.T. Yura, “Atmospheric turbulence induced laser beam spread,” Applied optics, vol. 10, iss. 12, pp.2771-2773, 1971. [6] A.K. Majumdar, J.C. Ricklin, “Free-Space Laser Communications Principles and Advances," New York : Springer, ISBN 978-0-387-28652-5. 2008.
Acknowledgement The research is connected to COST Action CA15220 Quantum Technologies in Space. The research was supported by the National Research Development and Innovation Office of Hungary (Project No. 2017-1.2.1-NKP-2017-00001).
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