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arXiv:0808.1265 · International Journal of Quantum Information

QUANTUM BIT ERROR RATE IN MODELED ATMOSPHERES

Nicolò Antonietti, M. Mondin, F. Daneshgaran, G. Giovanelli, Ivan Kirilov Kostadinov, Bruno Lunelli, G. Brida, Marco Genovese, Marco Gramegna

Published Jan 1, 2009• 4 citations
arXivHTMLPDF

Abstract

The quantum bit error rate is a key quantity in quantum communications. If the quantum channel is the atmosphere, the information is usually encoded in the polarization of a photon. A link budget is required, which takes into account the depolarization of the photon after its interaction with the atmosphere as well as absorption, scattering and atmospheric emissions. An experimental setup for the reproduction of a simple model of the atmosphere is used to evaluate the quantum bit error rate in a BB84 protocol and the results are presented. This result represents a first step toward the realization of an optical bench experiment where atmospheric effects are simulated and controlled for reproducing the effects on a quantum channel in different meteorological situations.

DOI
10.1142/s0219749909004591

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The quantum bit error rate is a key quantity in quantum communications. If the quantum channel is the atmosphere, the information is usually encoded in the polarization of a photon. A link budget is required, which takes into account the depolarization of the photon after its interaction with the atmosphere as well as absorption, scattering and atmospheric emissions. An experimental setup for the reproduction of a simple model of the atmosphere is used to evaluate the quantum bit error rate in a BB84 protocol and the results are presented. This result represents a first step toward the realization of an optical bench experiment where atmospheric effects are simulated and controlled for reproducing the effects on a quantum channel in different meteorological situations.
In the BB84 quantum key distribution (QKD) protocol, the communicating parties do a quantum bit error rate (QBER) test to determine whether there is an eavesdropper trying to gain information about the secret key. However, the QBER is not only influenced by the eavesdropper’s strategies, but also by the imperfections of the physical devices and the channel through which the quantum states propagate. We developed a simple channel model with error parameters describing the channel and the potential polarization switching in the transmitter, to see how those effects influence the QBER in a polarization-qubit BB84 implementation. Certain well-defined probabilistic channel models are compared to see which is responsible for the highest error probability.
Experimental results demonstrating long-term stability of the operation of our atmospheric quantum cryptography setup using the BB84 protocol and polarization coding are presented. It was shown that the “sifted” quantum key distribution rate and the quantum bit error rate in the key remained constant for 1 hour and were equal to 10 kbit/s and 6.5 %, respectively, at a distance between the transmitter and the receiver equal to 20 cm. Theoretical dependences of the secret quantum key generation rate on a quantum channel transmission coefficient for single-photon detectors, which were used in this experiment, and for new detectors with a reduced level of dark pulses are given.
The results of physical simulation of various optical disturbances in the atmospheric segment of a quantum wireless communication system are presented. Experimental setups for evaluating changes in the characteristics of the quantum key distribution system in an atmospheric communication channel in the presence of optical inhomogeneities in free-space (thermal zone disturbance, scattering water aerosol, incoming airflow) are described. Dynamic changes in quantum bit error rate (QBER) and the quantum sifted key generation rate under the influence of interfering disturbances in the atmospheric channel were obtained. It is determined that the strongest fluctuations in the characteristics of the quantum channel occurred when the source of disturbances was placed directly near the optical collimator connected to the quantum key distribution unit, which housed the single photon source.
Atmospheric conditions play a pivotal role in determining the performance of satellite-to-ground quantum key distribution (QKD). In this research, we meticulously investigate the influence of various factors, including background light, dark counts, and aperture coupling efficiency, on the performance of satellite-to-ground QKD under different levels of turbulence intensity associated with diverse atmospheric stratifications. Based on the decoy state BB84 protocol, we refine the calculation formula for the quantum bit error rate (QBER) of the satellite-to-ground QKD system. Subsequently, we conduct simulations to analyze how the quantum BER varies under different conditions, such as varying intensities of background light, different wavelengths, and different zenith angles. The simulation results reveal that, when taking all the above-mentioned factors into comprehensive consideration, employing signals with shorter wavelengths can lead to a more favorable QBER. The findings of this study offer valuable insights and a solid reference for the construction of a satellite-to-ground QKD system, facilitating the development of more reliable and efficient quantum communication links between space and the ground.
The efficient coupling of photons from a free-space quantum channel into a single-mode optical fiber (SMF) has important implications for quantum network concepts involving SMF interfaces to quantum detectors, atomic systems, integrated photonics, and direct coupling to a fiber network. Propagation through atmospheric turbulence, however, leads to wavefront errors that degrade mode matching with SMFs. In a free-space quantum channel, this leads to photon losses in proportion to the severity of the aberration. This is particularly problematic for satellite-Earth quantum channels, where atmospheric turbulence can lead to significant wavefront errors. This report considers propagation from low-Earth orbit to a terrestrial ground station and evaluates the efficiency with which photons couple either through a circular field stop or into an SMF situated in the focal plane of the optical receiver. The effects of atmospheric turbulence on the quantum channel are calculated numerically and quantified through the quantum bit error rate and secure key generation rates in a decoy-state BB84 protocol. Numerical simulations include the statistical nature of Kolmogorov turbulence, sky radiance, and an adaptive-optics system under closed-loop control.
The efficient coupling of photons from a free-space quantum channel into a single-mode optical fiber (SMF) has important implications to quantum network concepts involving SMF interfaces to quantum detectors, atomic systems, integrated photonics and direct coupling to a fiber network. Propagation through atmospheric turbulence however leads to wavefront errors that degrade mode-matching with SMFs. In a free-space quantum channel, this leads to photon losses in proportion to the severity of the aberration. This is particularly problematic for satellite-Earth quantum channels where atmospheric turbulence can lead to significant wavefront errors. This report considers propagation from a transmitter in low-Earth orbit to a terrestrial ground station and evaluates the efficiency with which photons couple either through a circular field stop or into a SMF situated in the focal plane of the optical receiver. The effects of atmospheric turbulence on the quantum channel are calculated numerically and quantified through the quantum bit error rate and secure key generation rates in a decoy-state BB84 protocol. Numerical simulations include the statistical nature of Kolmogorov turbulence, sky radiance, and an adaptive optics system under closed loop control.