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Scientific and technical journal of information technologies mechanics and optics

Synchronization signal distortion in subcarrier wave quantum key distribution systems

V.D. Dubrovskaia, Sergey A. Chivilikhin

Published Jul 12, 2017• 1 citation
Publisher

Abstract

Subject of Research.The paper deals with temperature effects dependence of the synchronization signal parameters in an optical fiber cable for a subcarrier wave quantum communication system. Two main causes of signal distortion are considered: the change in the refractive index as a function of the average daily temperature and the dispersion effects in the optical fiber, over which the signal is transmitted in the system. Method. To account for these effects, a temperature model has been created. The signal delay is calculated as a result of external influences in the system working with a standard fiber-optic cable. Real operational conditions are taken into account, including cable laying conditions, average daily temperature and wind speed. Main Results. The simulations were carried out on the standard single-mode fiber ITU-T G.652D. It was experimentally obtained that the maximum calculated phase mismatch of the synchronization signal for a system operating at a 100 km fiber length corresponds to a 1.7 ps signal time delay. The maximum operating intervals of the system without the use of phase adjustment are calculated. The obtained results are used to improve the parameters of the subcarrier wave quantum communication system. It is determined that the change in the refractive index in the fiber causes significant distortion of the signal. It is shown that stable operation is possible with adjustment every 158 ms. The additional phase delay resulting from the dispersion effects should be adjusted every 2.3 hours. Practical Relevance. The obtained results enable to optimize the parameters of the subcarrier wave quantum key distribution system to increase the overall key generation rate.

DOI
10.17586/2226-1494-2017-17-4-599-604

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An important problem in the practical implementation of fiber optical quantum communication systems is to synchronize the sender and receiver modules using a separate optical channel.The signal visibility in the quantum channel, which contributes to quantum bit error rate, is influenced by the synchronization signal delay.In this work, we investigate the dependence of the synchronization signal parameters on the dispersive effects in the fiber for a subcarrier wave quantum communication system (SCWQC), which is promising for quantum networking applications.The ITU-T G.652D standard single mode optical fiber was used for modeling.The maximum calculated phase mismatch of the synchronization signal for the system operating at 100 km fiber length corresponds to 1.7 ps signal time delay.The results show that dispersion causes significant signal distortion, therefore additional phase adjustment at least every 2.3 hours is required for stable system operation.
A common approach to establishing long-distance synchronization links in quantum communication (QC) systems is based on using optical signals transmitted in cables, where they decay and are distorted.It is necessary to evaluate the transformation of the signal parameters during propagation and their influence on the QC systems.We investigate the temperature dependence of the synchronization signal phase of a subcarrier wave quantum communication system (SCWQC) in optical fiber cables.A temperature model was created in order to determine the signal phase delay in the cable.We estimate the influence of daily temperature fluctuations on the phase delay in ground-and air-based cables.For systems operating with ground-based cables, they do not have any significant impact on the synchronization of the signal phase.However, for systems operating through air-based cables, phase adjustment is required every 158 ms for stable operation.This allowed us to optimize the parameters for a calibration procedure of a previously-developed SCWQC system, increasing the overall sifted key generation rate.
In this paper, we consider the influence of a divergence of polarization of a quantum signal transmitted through an optical fiber channel on the quantum bit error rate of the subcarrier wave quantum key distribution protocol. Firstly, we investigate the dependence of the optical power of the signal on the modulation indices' difference after the second phase modulation of the signal. Then we consider the Liouville equation with regard to relaxation in order to develop expressions of the dynamics of the Stokes parameters. As a result, we propose a model that describes quantum bit error rate for the subcarrier wave quantum key distribution depending on the characteristics of the optical fiber. Finally, we propose several methods for minimizing quantum bit error rate.
In this paper we investigate the chromatic dispersion impact on the quantum key distribution system based on multi-mode weak coherent phase-coded states. We provide an asymptotic secure key rate estimation, taking into account error detection probability due to chromatic dispersion. We demonstrate numerically and experimentally that the effect of chromatic dispersion in an optical fiber without any compensation hinders the secret key distribution at a distance more than 53 km. Finally, we propose a modification to the considered quantum communication system in order to mitigate the influence of chromatic dispersion on its performance.
This paper provides an in-depth theoretical analysis of subcarrier multiplexed quantum key distribution (SCM-QKD) systems, taking into account as many factors of impairment as possible and especially considering the influence of nonlinear signal mixing on the end-to-end quantum bit error rate (QBER) and the useful key rate. A detailed analysis of SCM-QKD is performed considering the different factors affecting the sideband visibility (drifts in the modulator bias points, modulation index mismatch between Alice and Bob subcarriers) and the impact of nonlinear signal mixing leaking into otherwise void subcarrier sidebands. In a similar way to classical photonic radio-over-fiber telecommunication and cable TV systems, the impact of this nonlinear signal mixing can be accounted in terms of a quantum carrier to noise ratio that depends on the specific frequency plan that is implemented. QBER and useful key rate results for three different frequency plans featuringNNN$=15(low−countchannelsystem),15 (low-count channel system),15(low−countchannelsystem),N$$=$30 (intermediate-count channel system), and$N$$=50(high−countchannelsystem)channelsareprovided,showingthatphotonnonlinearmixingcanbeofimportanceinmiddle−andhigh−countSCM−QKDsystems(50 (high-count channel system) channels are provided, showing that photon nonlinear mixing can be of importance in middle- and high-count SCM-QKD systems (50(high−countchannelsystem)channelsareprovided,showingthatphotonnonlinearmixingcanbeofimportanceinmiddle−andhigh−countSCM−QKDsystems(N≫30),withmoderateRFmodulationindexes(≫ 30), with moderate RF modulation indexes (≫30),withmoderateRFmodulationindexes(m≫5≫ 5%). In practical terms, nonlinear signal mixing can be neglected if low modulation indexes (≫5m$≪ 2%) are employed to encode the photons in the subcarrier sidebands.
Subject of study. An optical system, composed of transmitting and receiving telescopes, was designed for quantum key distribution, based on the subcarrier wave modulation method, over an atmospheric channel. Aim of study. The aim of the study was to develop an optical system that allowed the use of single-mode fibers as the input and output of the system, ensured the transmission of an ultralow-power optical signal without introducing additional distortion, and implemented a protocol for distributing a quantum key over an atmospheric optical communication channel at a distance of up to 25 m. Method. An experimental setup with an atmospheric quantum communication channel was developed, which showed stable quantum key distribution without interruptions throughout the measurement process. Radiation propagation simulations were also performed to estimate the insertion loss of the optical signal. Main results. Simulations revealed that the optical losses in the quantum key distribution system amounted to approximately 17 dB. The atmospheric communication channel was studied at distances of 5, 10, and 25 m. Considering all optical elements of the system, including the ferrules of the output and input fibers of the quantum key distribution modules, the attenuation of the optical signal was approximately 8, 13, and 18 dB, respectively. Based on the atmospheric optical losses, the quantum key generation rates were of the order of 500, 350, and 190 bits/s with increasing distance and insertion losses. The probability of a quantum error was in the range of 3% to 5%, which was lower than the threshold of 6%, ensuring the legitimacy of the generated key and excluding the possibility of an attack on the communication channel. Practical significance. The compatibility of the developed optical system with single-mode optical fibers allows its integration into the existing infrastructure of data transmission lines without the need for additional optical radiation converters. Owing to the analyzed characteristics of the optical system for distributing a quantum key over an atmospheric communication channel, it can be applied in communication systems based on the Internet of Things, unmanned vehicles, and other moving objects.