Polarization encoding has been extensively used in quantum key distribution (QKD) implementations along free-space links. However, the calculation model to characterize channel transmittance and quantum bit error rate (QBER) for free-space QKD has not been systematically studied. As a result, it is often assumed that misalignment error is equal to a fixed value, which is not theoretically rigorous. In this paper, we investigate the depolarization and rotation of the signal beams resulting from spatially-dependent polarization effects of the use of curved optics in an off-axis configuration, where decoherence can be characterized by the Huygens-Fresnel principle and the cross-spectral density matrix (CSDM). The transmittance and misalignment error in a practical free-space QKD can thus be estimated using the method. Furthermore, the numerical simulations clearly show that the polarization effect caused by turbulence can be effectively mitigated when maintaining good beam coherence properties.
Polarization encoding has been extensively used in quantum key distribution (QKD) implementations along free-space links. However, the calculation model to characterize channel transmittance and quantum bit error rate (QBER) for free-space QKD has not been systematically studied. As a result, it is often assumed that misalignment error is equal to a fixed value, which is not theoretically rigorous. In this paper, we investigate the depolarization and rotation of the signal beams resulting from spatially-dependent polarization effects of the use of curved optics in an off-axis configuration, where decoherence can be characterized by the Huygens-Fresnel principle and the cross-spectral density matrix (CSDM). The transmittance and misalignment error in a practical free-space QKD can thus be estimated using the method. Furthermore, the numerical simulations clearly show that the polarization effect caused by turbulence can be effectively mitigated when maintaining good beam coherence properties.
Abstract In this paper, we analyze the performance of free-space optical quantum key distribution (FSO-QKD) using the BB84 protocol with BPSK modulation under realistic channel conditions. The Málaga distribution is employed to model the composite atmospheric turbulence, considering pointing errors. We derive closed-form expressions for the average quantum bit error rate (QBER) and the secure key rate (SKR), incorporating both turbulence and misalignment effects. Numerical results demonstrate the impact of turbulence parameters and beam misalignment on system performance. The findings provide insights for the robust design of FSO-QKD systems under practical deployment conditions.
In polarization-encoding free-space Quantum Key Distribution (QKD), unwanted variations in the states of polarization may cause errors, leading to an increase in the quantum bit error rate (QBER), and a reduction of the Secure Key Rate (SKR). Optical elements that reflect or transmit the quantum signal at the transmitter and/or receiver are the main cause of polarization variations in the quantum states. Although most of these optical elements affect polarization in a constant manner, requiring relatively simple compensation techniques, mobile elements such as steering mirrors, cause time-varying polarization variations that are more complex to characterize and correct. In this work, we simulate the effect of steering mirrors’ typical values of angular rotation on the QBER. In particular, we show that, for most cases, an active correction of the polarization reference frame and a passive correction of the phase shift between the electric field components is sufficient to obtain QBER values due to the steering mirrors below 0.2%. This avoids the need of a fully active correction strategy, which increases the complexity, weight, and cost of the implementation. Furthermore, we present different design considerations to further reduce the steering mirrors’ contribution to the QBER (less than 0.05%).
Prepare-and-measure quantum key distribution (QKD) schemes with polarization encoding require the minimization of polarization degradation, i.e., undesired variations in the state of polarization, in the transmitter and receiver designs. In particular, the polarization extinction ratio (PER) should be maintained as high as possible to reduce the quantum bit error rate (QBER). In this paper, we analyze the polarization degradation and its correction in the design of free-space QKD systems. The polarization of a wavefront can be degraded in two different ways: uniformly, or non-uniformly; the latter known as polarization aberrations. While uniform polarization degradation of the beam wavefront can be easily corrected with standard retardation plates, polarization aberrations are more complex and require a different correction approach. BB84 diagonal linearly-polarized states are especially affected by polarization degradation as they are reflected off certain optical elements, and its correction is essential to achieve a low QBER. We have experimentally characterized the polarization degradation in a QKD transmitter and its impact in the QBER and achieved an almost perfect correction of the diagonal linearly polarized states when choosing a specific optical design.
Atmospheric turbulence poses a significant challenge to free-space measurement-device-independent quantum key distribution (FSO MDI-QKD) by inducing polarization decoherence and depolarization, which degrade the secret key rate (SKR). In this paper, we propose a unified depolarizing-dephasing channel model for turbulence-induced polarization decoherence in FSO MDI-QKD. This model consolidates phase perturbations, Gaussian beam spreading, beam drift, aperture truncation, and scintillation into closed-form parameters: depolarization factor, decoherence factor, and detection probability. By mapping turbulence to a von Mises-Fisher/Watson-distributed SU(2) rotation, we derive an analytic SKR expression compatible with existing MDI-QKD security analyses. The model excels in clear, overcast, and hazy weather conditions, offering computational efficiency and experimental verifiability for real-time link adaptation. Numerical simulations, illustrated on a ground-to-satellite free-space link, confirm its accuracy, enabling robust physical layer design for global-scale MDI-QKD networks.
This paper explores the secrecy performance of the recently proposed intensity modulation/direct detection (IM/DD) terrestrial free-space quantum key distribution (QKD) system, by using a Gaussian-beam propagation model and considering the combined effects of atmospheric turbulence and legitimate transceivers’ misalignment. Secrecy performance metrics including quantum bit error rate (QBER) and ergodic secret-key rate are newly derived in closedform expressions, taking into account all combined effects of turbulence- and misalignment-induced fading channels, the eavesdropper’s location relative to the legitimate receiver, and receiver noises. To satisfy security constraints, the system designs based on the intensity modulation depth and beam waist of the Gaussian beam at the transmitter, and dualthreshold (D-T) selection at the receiver, are comprehensively discussed under turbulence and misalignment conditions as well as different eavesdropper’s locations. Monte-Carlo (M-C) simulations are also implemented to verify the analytical results. Remarkably, this paper also offers the first framework in the literature to evaluate the secrecy performance of free-space optical (FSO) systems considering the eavesdropper’s location under the effect of misalignment between legitimate transceivers.
We devoted to analyzing information transfer in quantum channels in terms of the performance of quantum key distribution (QKD) free-space optical (FSO) communication systems through Bennett and Brassard 84 (BB84) protocol by taking into account the combined effect of attenuation, turbulence, pointing error, and angle of arrival (AOA) fluctuations. Path loss is modeled by Beer-Lambert law, and the turbulent channel is assumed to be Fisher-Snedecor F distributed. The pointing error and AOA fluctuations are modeled by Hoyt and Rayleigh distributions, respectively. The error and sift probabilities, quantum bit error rate, and secret key rate of a QKD FSO system are obtained in analytical form, and results are presented depending on various parameters. It is shown that increased beam waist, beam deviation, AOA fluctuations, and propagation distance cause performance degradation and less secure information transmission. However, an increase in the ratio of horizontal and vertical beam misalignments, field of view, average photon number per pulse, visibility of the atmospheric environment, and optical beam wavelength impact the performance of QKD FSO systems positively. The effect of the turbulence structure constant is observed to be modest on the performance of the QKD FSO system.