CC BY
11
i l St. Petersburg Polytechnic University Journal. Physics and Mathematics. 2022 Vol. 15, No. 3.2 Научно-технические ведомости СПбГПУ. Физико-математические науки. 15 (3.2) 2022
Conference materials UDC 535.51
DOI: https://doi.org/10.18721/JPM. 153.211
Influence of polarization reference frame rotation on ground-receiver error rate in satellite quantum key distribution
A. V. Duplinsky A. V. Khmelev V. E. Merzlinkin 23, V. L. Kurochkin ,2 3 4, Yu. V. Kurochkin ,2,34,5
1 QSpace Technologies, Moscow, Russia;
2 QRate, Moscow, Russia;
3 NTI Center for Quantum Communications, National University of Science and Technology MISiS, Moscow, Russia; 4 Russian Quantum Center, Moscow, Russia; 5 Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Region, Russia;
6 HSE University, Moscow, Russia H al.duplinsky@goqrate.com
Abstract. Quantum key distribution (QKD) in a space-Earth communication link is a difficult technical task. Aside from precise mutual pointing of the optical axes during the satellite QKD session, the polarization reference frame coincidence of the satellite and the receiving station is also required. Satellite motion causes a rotation of the polarization reference frame in respect to ground station measurements of quantum states, which contributes to the error rate in time. In order to reduce the quantum bit error rate, we designed and tested a polarization correction device for the receiving ground station that is included as a part of our data analysis and processing module. We have measured the polarization properties of the ground-based receiver and showed the evolution of four polarization states over time for a typical satellite passage. An average polarization extinction ratio is equal to 200:1 for the optical free-space receiver. We have calculated the maximum permitted deviation of the polarization reference frame at the performance of the compensation system, which is less than 5.8 degrees when bit error rate is equal to 1,5%.
Keywords: Quantum communications, quantum key distribution, polarimetry, extinction ratio, optical design, photon polarization, single photon detectors, free-space optics
Funding: Strategic academic leadership program "Priority 2030", indicating number of the financial support of K1-2022-027.
Citation: Duplinsky A. V., Khmelev A. V., Merzlinkin V.E., Kurochkin V. L., Kurochkin Yu. V., Influence of polarization reference frame rotation on ground-receiver error rate in satellite quantum key distribution, St. Petersburg State Polytechnical University Journal. Physics and Mathematics. 15 (3.2) (2022) 61-64. DOI: https://doi.org/10.18721/JPM.153.211
This is an open access article under the CC BY-NC 4.0 license (https://creativecommons. org/licenses/by-nc/4.0/)
Материалы конференции УДК 535.51
DOI: https://doi.org/10.18721/JPM. 153.211
Влияние вращения поляризационной системы отсчета на величину ошибок в эксперименте по квантовому распределению ключей со спутника на наземную станцию
А. В. Дуплинский ,26 н, А. В. Хмелев ,24, В. Е. Мерзлинкин 23, В. Л. Курочкин ,2 3 4, Ю. В. Курочкин ,2,34,5 1 КуСпэйс Технологии, г. Москва, Россия; 2 КуРэйт, г. Москва, Россия;
© Duplinsky A. V., Khmelev A. V., Merzlinkin V.E., Kurochkin V. L., Kurochkin Yu. V., 2022. Published by Peter the Great St.Petersburg Polytechnic University.
3 НТИ Центр Квантовых коммуникаций, Национальный Университет Науки и Технологии МИСиС, г. Москва, Россия;
4 Российский Квантовый Центр, г. Москва, Россия;
5 Московский физико-технический институт, г. Долгопрудный, Россия; 6 Национальный исследовательский университет «Высшая школа экономики», г. Москва, Россия
н al.duplinsky@goqrate.com
Аннотация. Квантовое распределение ключей по линии связи космос-Земля является сложной технической задачей. Помимо точного взаимного наведения оптических осей во время сеанса квантовой связи со спутником, также требуется совпадение поляризационной системы отсчета космического аппарата и приемной наземной станции. В статье представлены результаты тестов системы коррекции поляризации для наземной станции, которая входит в состав приемного модуля анализа и обработки данных. Проведены измерения поляризационных свойств наземной приемной станции для четырех поляризационных состояний от времени в ходе симуляции типичного пролёта спутника. Усредненный коэффициент поляризационной экстинкции для оптического приемника составил 200:1. Максимально допустимое отклонение поляризационной системы отсчета при работе системы компенсации составляет менее 5,8 градусов при ограничении итоговой величин ошибки в 1,5%.
Ключевые слова: Квантовые коммуникации, распределение квантовых ключей, поля-риметрия, коэффициент экстинкции, оптическая схема, поляризация фотонов, детекторы одиночных фотонов, оптика свободного пространства
Финансирование: Программа стратегического академического лидерства "Приори-тет-2030", проект № K1-2022-027.
Ссылка при цитировании: Дуплинский А. В., Хмелёв А. В., Мерзлинкин В. Е., Куроч-кин В. Л., Курочкин Ю. В. Влияние вращения поляризационной системы отсчета на величину ошибок в эксперименте по квантовому распределению ключей со спутника на наземную станцию // Научно-технические ведомости СПбГПУ. Физико-математические науки. 2022. Т. 15. № 3.2. С. 61-64. DOI: https://doi.org/10.18721/ JPM.153.211
Статья открытого доступа, распространяемая по лицензии CC BY-NC 4.0 (https:// creativecommons.org/licenses/by-nc/4.0/)
Introduction
Quantum key distribution in a Space-Earth optical communication link is a challenging technical task [1,2]. The development of an equipment requires a solution of many issues including the precise optical axes pointing of a ground station and a satellite payload, but also the highly necessary polarization reference frame coincidence of them. The problem of pointing and tracking is successfully solved in our previous articles [3,4]. The solution to the polarization rotation problem is reported here.
The satellite reference frame has a time dependent rotation relatively at the ground station, even when the satellite system is stabilized along the nadir axis [5]. Such angular movement creates a shift in the angles of the polarization bases during a QKD communication with the satellite, which increases the error rate when decoding quantum states.
In this work we consider the effect of a time dependent rotation of the polarization basis and describe the method which helps to compensate this polarization deviation. The observed polarization characteristic of an optical ground station allows us to determine the maximum mismatch angle of polarization reference frames encoding and decoding photon states.
Methods
A ground-based receiver for QKD is located in the Zvenigorod observatory, about 80 km from Moscow. A Ritchey-Chretien Alt-Az telescope with an aperture of 0.6 m and a focal length of 4.8 m is used to gather a quantum signal. The main optical part of the receiver for satellite quantum key distribution with a satellite consists of a mirror telescope, an optical signal processing unit, and a polarization analyzer (PA).
© Дуплинский А. В., Хмелёв А. В., Мерзлинкин В. Е., Курочкин В. Л., Курочкин Ю. В., 2022. Издатель: Санкт-Петербургский политехнический университет Петра Великого.
4
Simulation of physical processes
The polarization analyzer acts as a free-space decoder of quantum states that allows using the BB84 protocol for satellite-to-ground QKD. The optical signal analysis and processing system (APS) includes a motorized half-wave plate. Its time-dependent angular motion may be regulated by a predicted function to correct the rotation of the reference frame of polarization bases measurements, as shown in figure 1. By altering the angle of the half-wave plate fast axis, a unit can align the decoder's polarization reference frame in relation to the transmitter's polarized photons.
In order to test the compensating system, we simulate the relative rotation of the satellite to the Alt-Azimuth telescope polarization reference frame. A polarized laser source with an intense output power and a wavelength of roughly 850 nm is positioned in front of our receiving ground station. This source is mounted in a high-precision rotary holder, altering the angle of the output linear polarization.
Firstly, we should define the zero point of our receiver, setting a horizontal |H)-polarization on the laser source. Rotating the half-wave plate of the compensation system in APS, we find its angular position that corresponds to the maximum number of clicks on the single photon detector coupled to the |H)-channel of the polarization decoder.
Fig. 1. Polarization conversion in APS module
To obtain the expected error rate of the ground station, we measure the polarization characteristics of the optical receiver using an intense laser source with a polarization extinction ratio (PER) better than 4000:1. So, we start a polarization rotation of the laser source in a range of ±90 degrees according to the predicted function and compensate it on the receiver, simultaneously. Such measurements are carried out for |H) — horizontal polarization, |V) — vertical polarization, |D) — diagonal polarization and |A) — anti-diagonal polarization decoder channels. The Fig.2. Polarization extinction ratio (PER) obtained in the results of polarization extinction
local test coefficient depending on time for
these channels are presented in figure 2. The average value of the PER of these polarization states for our setup turned out to be less than 0.5% (Fig. 2).
Results
Based on the PER values acquired from experiment for the stationary transmission of polarization states, the compensating mechanism appears to be operational. Because the simulation of the satellite QKD session was conducted in the presence of a strong optical signal, we can only estimate the optical QBER of our system without taking noise into account.
Let us estimate the permissible angular error of polarization reference frame rotation when the
upper bound of expected QBER is under 1.5%:
QBERexp = QBERopt + ERLi sin2 0 _, (i)
ER + 1
where ER — reciprocal of average PER, 0 — angular error value, QBER - the specified (expected) limit parameter for error rate, QBER pt — optical part of error rate.
Hence, taking into account eR = 200 from local polarization test and consequently QBER = 0.5%, QBER = 1.5 %, we can calculate 0 , using estimated and experimental
opt ' exp ? max? w A
measurements as follows: _
0 . I(ER +1)- QBERopt
0_ = arcsin y-—-, (2)
0 = 5.78°. (3)
max y
Conclusion
We have demonstrated the work of the analysis and processing module in operating mode simulation. The APS module can successfully compensate for polarization reference frame rotation and the average optical QBER is 0.5%. Finally, we estimate the maximum allowed angular error for the compensation system, as a consequence of complexity of the precise satellite rotation prediction.
Acknowledgments
We would like to thank colleagues at the Institute of Astronomy of the Russian Academy of Sciences for their assistance and support in the form of the strategic academic leadership program "Priority 2030", indicating number of the financial support of K1-2022-027.
REFERENCES
1. Liao, Sheng-Kai, et al., Satellite-to-ground quantum key distribution. Nature 549.7670 (2017) 43-47.
2. Han, Xuan, et al., Polarization design for ground-to-satellite quantum entanglement distribution. Optics Express 28.1 (2020) 369-378.
3. Khmelev, A. V., et al., Recording of a Single-Photon Signal from Low-Flying Satellites for Satellite Quantum Key Distribution. Technical Physics Letters (2021) 1-4.
4. Kurochkin, V. L., et al., Elements of satellite quantum network. International Conference on Micro-and Nano-Electronics 2021. Vol. 12157. SPIE, 2022.
5. Zhang, Ming, et al., Detection and compensation of basis deviation in satellite-to-ground quantum communications. Optics express 22.8 (2014) 9871-9886.
THE AUTHORS
DUPLINSKY Alexey V. KUROCHKIN Vladimir L.
al.duplinsky@goqrate.com v.kurochkin@rqc.ru
ORCID: 0000-0002-2964-1800 ORCID: 0000-0002-1599-9801
KHMELEV Aleksandr V. KUROCHKIN Yury V.
a.khmelev@goqrate.com yk@goqrate.com
ORCID: 0000-0003-1511-1128 ORCID: 0000-0001-5376-6358
MERZLINKIN Vitalii E.
merzlinkin@yandex.ru
ORCID: 0000-0002-4310-2619
Received 15.08.2022. Approved after reviewing 08.09.2022. Accepted 08.09.2022.
© Peter the Great St. Petersburg Polytechnic University, 2022
