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Stabilization of transmittance fluctuations caused by beam wandering in continuous-variable quantum communication over free-space atmospheric channels

Usenko, V., Peuntinger, C., Heim, B., Günthner, K., Derkach, I., Elser, D., Marquardt, C., Filip, R., Gerd Leuchs

Published Nov 26, 2018• 23 citations
OpenAlex

Abstract

Transmittance fluctuations in turbulent atmospheric channels result in quadrature excess noise which limits applicability of continuous-variable quantum communication. Such fluctuations are commonly caused by beam wandering around the receiving aperture. We study the possibility to stabilize the fluctuations by expanding the beam, and test this channel stabilization in regard of continuous-variable entanglement sharing and quantum key distribution. We perform transmittance measurements of a real free-space atmospheric channel for different beam widths and show that the beam expansion reduces the fluctuations of the channel transmittance by the cost of an increased overall loss. We also theoretically study the possibility to share an entangled state or to establish secure quantum key distribution over the turbulent atmospheric channels with varying beam widths. We show the positive effect of channel stabilization by beam expansion on continuous-variable quantum communication as well as the necessity to optimize the method in order to maximize the secret key rate or the amount of shared entanglement. Being autonomous and not requiring adaptive control of the source and detectors based on characterization of beam wandering, the method of beam expansion can be also combined with other methods aiming at stabilizing the fluctuating free-space atmospheric channels.

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Transmittance fluctuations in turbulent atmospheric channels result in quadrature excess noise which limits applicability of continuous-variable quantum communication. Such fluctuations are commonly caused by beam wandering around the receiving aperture. We study the possibility to stabilize the fluctuations by expanding the beam, and test this channel stabilization in regard of continuous-variable entanglement sharing and quantum key distribution. We perform transmittance measurements of a real free-space atmospheric channel for different beam widths and show that the beam expansion reduces the fluctuations of the channel transmittance by the cost of an increased overall loss. We also theoretically study the possibility to share an entangled state or to establish secure quantum key distribution over the turbulent atmospheric channels with varying beam widths. We show the positive effect of channel stabilization by beam expansion on continuous-variable quantum communication as well as the necessity to optimize the method in order to maximize the secret key rate or the amount of shared entanglement. Being autonomous and not requiring adaptive control of the source and detectors based on characterization of beam wandering, the method of beam expansion can be also combined with other methods aiming at stabilizing the fluctuating free-space atmospheric channels.
Transmittance fluctuations in turbulent atmospheric channels result in quadrature excess noise which limits applicability of continuous-variable quantum communication. Such fluctuations are commonly caused by beam wandering around the receiving aperture. We study the possibility to stabilize the fluctuations by expanding the beam, and test this channel stabilization in regard of continuous-variable entanglement sharing and quantum key distribution. We perform transmittance measurements of a real free-space atmospheric channel for different beam widths and show that the beam expansion reduces the fluctuations of the channel transmittance by the cost of an increased overall loss. We also theoretically study the possibility to share an entangled state or to establish secure quantum key distribution over the turbulent atmospheric channels with varying beam widths. We show the positive effect of channel stabilization by beam expansion on continuous-variable quantum communication as well as the necessity to optimize the method in order to maximize the secret key rate or the amount of shared entanglement. Being autonomous and not requiring adaptive control of the source and detectors based on characterization of beam wandering, the method of beam expansion can be also combined with other methods aiming at stabilizing the fluctuating free-space atmospheric channels.
Abstract We investigate estimation of fluctuating channels and its effect on security of continuous-variable quantum key distribution. We propose a novel estimation scheme which is based on the clusterization of the estimated transmittance data. We show that uncertainty about whether the transmittance is fixed or not results in a lower key rate. However, if the total number of measurements is large, one can obtain using our method a key rate similar to the non-fluctuating channel even for highly fluctuating channels. We also verify our theoretical assumptions using experimental data from an atmospheric quantum channel. Our method is therefore promising for secure quantum communication over strongly fluctuating turbulent atmospheric channels.
Atmospheric turbulence is one of the lead disturbance factors for free-space quantum communication. The quantum states of light in such channels are affected by fluctuating losses characterized by the probability distribution of transmittance (PDT). We obtain the PDT for different horizontal links via numerical simulations of light transmission through the atmosphere. The results are compared with analytical models: the truncated log-normal distribution, the beam-wandering model, the elliptic-beam approximation, and the model based on the law of total probability. Their applicability is shown to be strongly dependent on the receiver aperture radius. We introduce an empirical model based on the Beta distribution, which is in good agreement with numerical simulations for a wide range of channel parameters. However, there are still scenarios where none of the above analytical models fits the numerically simulated data. The numerical simulation is then used to analyze the transmission of quadrature-squeezed light through free-space channels.
Many fundamental and applied experiments in quantum optics require transferring nonclassical states of light through large distances. In this context the free-space channels are a very promising alternative to optical fibers as they are mobile and enable to establish communications with moving objects, using satellites for global quantum links. For such channels the atmospheric turbulence is the main disturbing factor. The statistical properties of the fluctuating transmittance through the turbulent atmosphere are given by the probability distribution of transmittance (PDT). We derive the consistent PDTs for the atmospheric quantum channels by step-by-step inclusion of various atmospheric effects such as beam wandering, beam broadening and deformation of the beam into elliptic form, beam deformations into arbitrary forms. We discuss the applicability of PDT models for different propagation distances and optical turbulence strengths in the case when the receiver module has an annular aperture. We analyze the optimal detection and correction strategies which can improve the channel transmission characteristics. The obtained results are important for the design of optical experiments including postselection and adaptive strategies and for the security analysis of quantum communication protocols in freespace.
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 investigate the decoy state quantum key distribution via the atmosphere channels. We consider the efficient decoy state method with one-signal state and two-decoy states. Our results show that the decoy state method works even in the channels with fluctuating transmittance. Nevertheless, the key generation rate will be dramatically decreased by atmosphere turbulence, which sheds more light on the characterization of atmosphere turbulence in realistic free-space based quantum key distributions.