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Nanosystems Physics Chemistry Mathematics

On quantum bit coding by Gaussian beam modes for the quantum key distribution

Maria P. Faleeva, I. Yu. Popov

Published Dec 30, 2020• 6 citations
Publisher

Abstract

This paper deals with possibility of implementation of quantum key distribution algorithm through turbulent atmosphere.Beam wandering is considered as the main perturbation.For description of the density matrix, the Glauber-Sudarshan P-function technique is used.The probabilities of detectors triggering are determined.
DOI
10.17586/2220-8054-2020-11-6-651-658

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The atmospheric turbulence is the main factor that influences quantum properties of propagating optical signals and may sufficiently degrade the performance of quantum communication protocols. The probability distribution of transmittance (PDT) for free-space channels is the main characteristic of the atmospheric links. Applying the law of total probability, we derive the PDT by separating the contributions from turbulence-induced beam wandering and beam-spot distortions. As a result, the obtained PDT varies from log-negative Weibull to truncated log-normal distributions depending on the channel characteristics. Moreover, we show that the method allows one to consistently describe beam tracking, a procedure which is typically used in practical long-distance free-space quantum communication. We analyze the security of decoy-state quantum key exchange through the turbulent atmosphere and show that beam tracking does not always improve quantum communication.
We consider the properties of a quantum communication channel in open space using the superdense coding algorithm as an example. We studied the theoretical model of the installation that implements this algorithm, and identified the main factors affecting the quality of the model. Among them is the atmospheric transmittance, the efficiency of detectors, and the average value of the number of noise counts caused by background radiation and dark counts. We made a complete calculation of the installation model and obtained explicit results. These results were analyzed using realistic parameters of detectors and the atmosphere. It was found that the atmospheric turbulence instability, detectors efficiency and the average value of noise counts have the greatest influence on the results.
High-speed free-space quantum key distribution located in urban environment offers an interesting alternative to public key encryption - whose security strength is yet to be mathematically proven. To achieve this, three main objectives need to be accomplished: both the emitter and receiver have to be capable of transmitting and receiving at high speed - with the selection of the source's wavelength and detectors being of especial importance - the error rate needs to be kept at a minimum, especially that due to solar background radiation; and finally, a fast automatic tracking system, capable of compensating for atmospheric turbulence effects, is needed. Regarding to sky background and atmospheric turbulence, two different tracking techniques involving the beam wander compensation in the emitter or the receiver are presented and one of them is selected for our system, based on the link propagation distance and the atmospheric turbulence regime.