CC BY
5
i l St. Petersburg Polytechnic University Journal. Physics and Mathematics. 2022 Vol. 15, No. 3.3 Научно-технические ведомости СПбГПУ. Физико-математические науки. 15 (3.3) 2022
Conference materials UDC 535.51
DOI: https://doi.org/10.18721/JPM.153.339
Polarization compensation design for free-space quantum communication transmitter
V. E. Merzlinkin 2, 3e, A. V. Khmelev 2, 4, 5, A. V. Duplinsky 2, 6, V. L. Kurochkin 2, 3, 4, Yu. V. Kurochkin 2, 3, 4, 5
1 LLC "QSpace Technologies", Moscow, Russia; 2 LLC "QRate", Moscow, Russia; 3 National University of Science and Technology MISiS, Moscow, Russia; 4 Russian Quantum Center, Moscow, Russia; 5 Moscow Institute of Physics and Technology, Dolgoprudny, Russia; 6 National Research University Higher School of Economics, Moscow, Russia H v.merzlinkin@goqrate.com Abstract. Quantum communication is a transmission technology that allows legitimate users to share a secret key. The BB84 protocol employs four linear polarization states for encoding in our quantum key distribution system. However, the optical elements affect the polarization features of quantum state, which leads to errors in decoded key. To reduce mistakes and increase device encoding performance, a polarization controller is included in the optical circuit. An algorithm identifying the angles of the polarization controller's wave plates has been developed. We conclude that using a polarization controller and the method of finding angles has improved the polarization extinction ration for all encoding channels of designed free-space transmitter. Finding angles of the plates is a problem of optimizing the search for parameters where the trace of matrix is maximum in the Stokes-Muller formalism. We used the gradient descent approach to determine the angles of the plates and we were able to obtain optical part of QBER values of 0.12 percent, so decreasing its values by 185 times.
Keywords: quantum communications, quantum key distribution, BB84 protocol, polarization controller, phase shift, the Poincare sphere, polarimetry
Funding: The strategic academic leadership program "Priority 2030", indicating number of the financial support of K1-2022-027.
Citation: Merzlinkin V. E., Khmelev A. V., Duplinsky A. V., Kurochkin V. L., Kurochkin Yu. V., Polarization compensation design for free-space quantum communication transmitter. St. Petersburg State Polytechnical University Journal. Physics and Mathematics, 15 (3.3) (2022) 202-206. DOI: https://doi.org/10.18721/JPM.153.339
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.153.339
Квантовый передатчик в открытом пространстве с компенсацией искажений поляризации
В. Е. Мерзлинкин 1 2, 3Н, А. В. Хмелев 1 2, 4, 5, А. В, Дуплинский 1 2, 6, В. Л. Курочкин ', 2, 3, 4, Ю. В. Курочкин 1 2, 3, 4, 5
1 OOO «КуСпэйс Технологии», Москва, Россия; 2 ООО «КуРэйт», Москва, Россия; 3 Национальный исследовательский технологический университет МИСиС, Москва, Россия; 4 Российский Квантовый Центр, Москва, Россия;
© Merzlinkin V. E., Khmelev A. V., Duplinsky A. V., Kurochkin V. L., Kurochkin Yu. V., 2022. Published by Peter the Great St.Petersburg Polytechnic University.
5 Московский физико-технический институт, Долгопрудный, Россия;
6 Национальный исследовательский университет «Высшая школа экономики», Москва, Россия
н v.merzlinkin@goqrate.com
Аннотация. Квантовая коммуникация — это технология передачи, позволяющая обмениваться секретным ключом авторизованным пользователям. Протокол квантового распределения ключа BB84 использует четыре состояния линейной поляризации для кодирования, но оптические элементы влияют на поляризацию, что приводит к ошибкам в квантовом ключе при его декодировании. Поляризационный контроллер позволяет снизить величину такой ошибки в ключе. В результате, мы разработали алгоритм определения углов волновых пластин контроллера поляризации, позволяющий компенсировать влияние оптических элементов на поляризационные состояния фотонов. Поиск углов пластинок был осуществлен через решение задачи оптимизации нахождения параметров, где матрица в формализме Стокса-Мюллера имела максимальный след. Найденные углы позволили снизить оптическую часть QBER/а до значения 0.12%, что в 185 раз ниже, чем изначальный.
Ключевые слова: квантовые коммуникации, квантовое распределение ключей, BB84 протокол, контроллер поляризации, фазовый сдвиг, сфера Пуанкаре, поляриметрия
Финансирование: Программа стратегического академического лидерства «Приоритет-2030», проект № К1-2022-027.
Ссылка при цитировании: Мерзлинкин В. Е., Хмелев А. В., Дуплинский А. В., Курочкин В. Л., Курочкин Ю. В. Квантовый передатчик в открытом пространстве с компенсацией искажений поляризации // Научно-технические ведомости СПбГПУ. Физико-математические науки. 2022. Т. 15. № 3.3. C. 202-206. DOI: https://doi. org/10.18721/JPM.153.339
Статья открытого доступа, распространяемая по лицензии CC BY-NC 4.0 (https:// creativecommons.org/licenses/by-nc/4.0/)
Introduction
Quantum communication is studied by a large number of scientific groups as one of the reliable and promising methods in the information security [1, 2]. Significant progress has been achieved in the development of systems and their theoretical analysis for the quantum key distribution (QKD) since the first concept was proposed [3]. However, practical realization of quantum key distribution systems are imperfect, and this fact opens up many opportunities for eavesdropping [4]. To achieve a high-secure communication, researchers propose different protocols and optical schemes to share secret key [5].
The high losses of single photons that propagates across a medium are also one of the main problems for the quantum cryptography implementation for a long distance. Nowadays, cutting-edge QKD experiment provides an adequate key rate at distance up to 250 km in an optical fiber [6]. To perform a long-distance quantum key distribution, the most preferable realization is a free-space system using polarization coding method of photon states [7]. Commonly, the BB84 decoy-state protocol is the most practically useful for free-space quantum communication based on the linear polarization states: |H>, |V>, |D> = 1 V2 (|H> + |V>), |A> = 1 V2 (|H> - |V>).
The transmitter using polarization encoding has to provide high linearity and unbiased bases output photon states. However, the polarization light can be affected by the imperfection of the optical elements and their dependence on incident angle of the polarization light. Therefore, polarization compensation of photons is one of the essential technology to decrease the level of errors while decoding quantum states. We report the results of polarization characteristics of designed transmitter for free-space quantum communication. The polarization properties of optical elements in transmitter have been investigated and algorithm for a polarization controller made up of one half-wave plate (HWP) and two quarter-wave plate (QWP) has been developed.
Optical systems can introduce dissipative and phase losses. Dissipative polarization losses are the rotation of one of the bases relative to the other, for example due to the large absorption of "s" or "p" polarization. Phase loss is the phase shift between the "s" or "p" of polarization, which
© Мерзлинкин В. Е., Хмелев А. В., Дуплинский А. В., Курочкин В. Л., Курочкин Ю. В., 2022. Издатель: Санкт-Петербургский политехнический университет Петра Великого.
^St. Petersburg Polytechnic University Journal. Physics and Mathematics. 2022 Vol. 15, No. 3.3 ^
leads to ellipticity of polarization in the diagonal basis [8]. Dissipative losses are insignificant in our QKD optical systems, therefore, as part of the work, measures were taken to eliminate the phase error.
Incorrect measurements in QKD can be associated with two reasons, with imperfect equipment and an attacker's intrusion in the quantum channel. To evaluate the first, we introduce such a concept as a quantum bit error rate (QBER). The QBER is affected of two parts: noise counts and optical part.
Method
The transmitter using polarization encoding has to provide high linearity and unbiased bases output photon states. However, the polarization light can be affected by the imperfection of the optical elements and their dependence on incident angle of the polarization light. As a result, one of the most important ways to decrease quantum bit error rate (QBER) is a method of photon polarization compensation for the transmitter.
Laboratory measurements of the optical transmitter were shown strong polarization distortions caused by MEMS and two dichroic mirrors. These mirrors perform important functions, such as accurate alignment of the system and separation of communication channels. To compensate for the error caused by them, we utilize a polarization controller with one half-wave plate (HWP) and two quarter-wave plates (QWP). The algorithm of working with it was written based on the Stokes-Mueller formalism and include solving the optimization problem. The algorithm for finding the angles of wave plates finds the maximum of the function (1) using the gradient descent method.
1 Tr[SMx (x)M 2 (y)M 4 (z)] = 1 (1)
4
where S is matrix describing the effect of an optical system on polarization; M is wave plate matrix; x, y, z are angles of the plates.
—*---1 —
T
I i
A,
Fig. 1. The scheme of the quantum communication transmitter: 1, 9 — polarizing beam splitters; 2 — half—wave plate; 3 — beam splitters 50:50; 4 — dichroic mirror DLMP805R; 5 — dichroic mirror DMSP805T; 6 — MEMS mirror; 7, 8 — linear polarizers; V, H, D, A — vertical, horizontal, diagonal, antidiagonal polarization of the photons; dotted line — optical path of the laser beam with
wavelength 850 nm
The quantum transmitter circuit, as shown in Fig. 1, was created for the QKD nanosatellite, where there is an acute problem with the size and efficient use of volume. The polarization controller was placed between the beam splitter and the dichroic mirror.
Results
Table 1 shows the improvements in the polarization parameters of the QKD transmitter that we have achieved in our work. It is possible to notice worsening in the parametrs in the direct basis (horizontal and vertical polarization), this is due to the fact that the wave plates are not ideal and have their own permissions. Optical part of QBER was calculated using the equation (2).
Fig. 2 demonstrates a visual interpretation of the results obtained through the Poincare sphere and the polarization ellipse.
QBER =
^ opt
1
' i=V,H,A,D
where 0 is ellipticity of polarization.
tg +1
(2) Table 1
Results of measurements of polarization's ellipticity and calculated QBER
opt
© wV © H ©D ©A QBEROBt
Without polarization controller 2.3° 1.6° 40.3° 42.7° 22%
With polarization controller 3.01° 2.13° 1° 1° 0.12%
Notations: 0. — elipcicty of state polarization, QBERopt — optical part of QBER.
Fig. 2. Visualization of the light polarization in a diagonal basis. The initial polarization at the system's
output is depicted in red; and after compensation procedure using controller is shown in blue.
1 — Section of the Poincare sphere; 2 — Polarization ellipse
Conclusion
We have reported the results of polarization characteristics of designed transmitter for freespace quantum communication. The polarization properties of optical elements in transmitter have been investigated and algorithm for a polarization controller made up of one half-wave plate (HWP) and two quarter-wave plate (QWP) has been developed. We have obtained the improvement of the QBERopt at 185 times.
REFERENCES
1. Dowling Jonathan P., Gerard J. Milburn., Quantum technology: the second quantum revolution. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 361. 1809 (2003) 1655-1674.
2. Sidhu, J. S., et al., Advances in space quantum communications. IET Quant. Comm. 2 (4) (2021) 182-217.
3. Bennett C. H., Brassard G., Quantum cryptography: public key distribution and coin tossing, Proceedings of the IEEE International Conference on Computers, Systems & Signal Processing, (1984) 175-179.
4. Sun Shihai, Anqi Huang, A Review of Security Evaluation of Practical Quantum Key Distribution System, Entropy. 24 (2) (2022) 260.
5. Bedington R., Arrazola J. M., Ling A., Progress in satellite quantum key distribution. npj Quantum Information. 3.1 (2017) 1-13.
6. Zhang, Yichen, et al., Long-distance continuous-variable quantum key distribution over 202.81 km of fiber. Physical review letters. 125.1 (2020) 010502.
7. Toyoshima Morio, et al., Polarization-basis tracking scheme in satellite quantum key distribution. International Journal of Optics, 2011.
8. Wu Jincai, et al., Polarization study about a telescope-based transmitter for quantum communication. Applied Optics. 56.30 (2017) 8501-8506.
St. Petersburg Polytechnic University Journal. Physics and Mathematics. 2022 Vol. 15, No. 3.3
THE AUTHORS
МERZLINKIN Vitalii E.
v.merzlinMn@goqrate.com ORCID: 0000-0002-4310-2619
KHMELEV Aleksandr V.
a.khmelev@goqrate.com ORCID: 0000-0003-1511-1128
DUPLINSKY Alexey V.
a.duplinsky@gmail.com ORCID: 0000-0002-2964-1800
KUROCHKIN Vladimir L.
v.kurockin@goqrate.com ORCID: 0000-0002-1599-9801
KUROCHKIN Yury V.
yk@goqrate.com
ORCID: 0000-0001-5376-6358
Received 15.08.2022. Approved after reviewing 24.08.2022. Accepted 24.08.2022.
© Peter the Great St. Petersburg Polytechnic University, 2022
