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The Influence of Signal Polarization on Quantum Bit Error Rate for Subcarrier Wave Quantum Key Distribution Protocol

Andrei Gaidash, Козубов Антон Владимирович, Svetlana Medvedeva, George P. Miroshnichenko

Published Dec 9, 2020• 4 citations
Publisher

Abstract

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.

DOI
10.3390/e22121393

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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.
A quantum key distribution system based on the subcarrier wave modulation method has been demonstrated which employs the BB84 protocol with a strong reference to generate secure bits at a rate of 16.5 kbit/s with an error of 0.5% over an optical channel of 10 dB loss, and 18 bits/s with an error of 0.75% over 25 dB of channel loss. To the best of our knowledge, these results represent the highest channel loss reported for secure quantum key distribution using the subcarrier wave approach. A passive unidirectional scheme has been used to compensate for the polarization dependence of the phase modulators in the receiver module, which resulted in a high visibility of 98.8%. The system is thus fully insensitive to polarization fluctuations and robust to environmental changes, making the approach promising for use in optical telecommunication networks. Further improvements in secure key rate and transmission distance can be achieved by implementing the decoy states protocol or by optimizing the mean photon number used in line with experimental parameters.
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.
In this work we consider the Liouville equation; it describes the dynamics of the photon density matrix in the Schr\"odinger representation based on the Markov approximation in the channel without dispersion. The equation contains a relaxation superoperator dependent on the phenomenological parameters of the optical fiber. These parameters allow one to take into account the phenomena of birefringence and optical activity, isotropic absorption, and dichroism. We also present in our work that these parameters affect not only the polarization of the states but the length of the Stokes vector. Hence the developed technique describes the decoherence process in the polarization domain in the quantum case and allows one to analyze the dynamics of single-photon states in the quantum (depolarizing) channel more properly. We also present a visual illustration of polarization states' evolution in the polarization-coded quantum key distribution BB84 protocol as an example. We estimate quantum bit error rates' dependence on channel length. Also we examine maximal allowed channel length, dependent on various configurations of channel parameters.
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.
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.