In coherent optical communication across turbulent atmospheric channels, reference beacons can be multiplexed with information-encoded signals during transmission. In this case, it is commonly assumed that the wavefront distortion of the two is equivalent. In contrast to this assumption, we present experimental evidence of relative wavefront errors (WFEs) between polarization-multiplexed reference beacons and signals, after passing through a 2.4-km atmospheric link. We develop machine learning (ML)-based wavefront correction algorithms to compensate for observed WFEs, via phase retrieval, resulting in up to a 2/3 reduction in the relative phase error variance. Further, we analyze the excess noise contributions from relative WFEs in the context of continuous-variable quantum key distribution (CV-QKD), where our findings suggest that if future CV-QKD implementations employ wavefront correction algorithms similar to those reported here, an order of magnitude increase in secure key rates may be forthcoming.
In coherent optical communication across turbulent atmospheric channels, reference beacons can be multiplexed with information-encoded signals during transmission. In this case, it is commonly assumed that the wavefront distortion of the two is equivalent. In contrast to this assumption, we present experimental evidence of relative wavefront errors (WFEs) between polarization-multiplexed reference beacons and signals, after passing through a 2.4-km atmospheric link. We develop machine learning (ML)-based wavefront correction algorithms to compensate for observed WFEs, via phase retrieval, resulting in up to a 2/3 reduction in the relative phase error variance. Further, we analyze the excess noise contributions from relative WFEs in the context of continuous-variable quantum key distribution (CV-QKD), where our findings suggest that if future CV-QKD implementations employ wavefront correction algorithms similar to those reported here, an order of magnitude increase in secure key rates may be forthcoming.
This thesis investigates how machine learning (ML) can assist state-of-the-art continuous-variable quantum key distribution (CV-QKD) protocols to advance a global Quantum Internet. Relative wavefront errors between multiplexed classical reference pulses and quantum signals pose a significant challenge to the practical implementation of a satellite-Earth CV-QKD network across turbulent atmospheric channels, potentially leading to the destruction of secure key transfer. ML is proposed as a solution, where ML-based wavefront correction algorithms are designed to mitigate the potentially deleterious effects of relative wavefront errors on CV-QKD, as a result of excess noise affecting the quantum signals. This thesis provides the first analysis of two-dimensional spatial relative wavefront errors. The potential causes of relative wavefront errors are explored, their evolution across satellite-Earth channels is simulated, and their effect on achievable secure key rates is evaluated. ML-based wavefront correction algorithms are designed to facilitate enhanced key rates by encoding the wavefront corrections onto a real local oscillator at the receiver. The analysis of relative wavefront errors presented in this thesis culminates in a series of experimental campaigns involving the transmission of multiplexed stronger reference signals and weaker signals across a 2.4~km free-space optical link, providing the first experimental evidence of relative wavefront errors in the context of CV-QKD. Modified ML-based wavefront correction algorithms are then applied to the experimental data, using phase retrieval, resulting in up to a 2/3 reduction in relative phase error variance. Overall, it is shown that ML algorithms can augment state-of-the-art CV-QKD protocols across turbulent atmospheric channels, thereby progressing the practical feasibility of developing a truly global CV-QKD network.
When undertaking continuous-variable quantum key distribution (CV-QKD) across atmospheric channels, strong classical local oscillators (LOs) are often polarization-multiplexed with the weak quantum signals for coherent measurement at the receiver. Although the wavefronts of the quantum signal and LO are often assumed to experience the same distortion across channels, previous theoretical work has shown that they can experience differential distortions, resulting in relative wavefront errors (WFEs). Such errors have previously been shown to limit CV-QKD performance, in some cases leading to zero secure key rates. In this work, for the first time, we provide strong experimental evidence that relative WFEs are present in some circumstances and that standard assumptions in CVQKD deployments may need to be revisited. In addition, we demonstrate how turbulence can affect the detailed form of the relative WFEs, thereby indicating that long-range links like terrestrial-satellite channels are likely impacted more than shortrange terrestrial-only channels.
ABSTRACT State‐of‐the‐art free‐space continuous‐variable quantum key distribution (CV‐QKD) protocols use phase reference pulses to modulate the wavefront of a real local oscillator at the receiver, thereby compensating for wavefront distortions caused by atmospheric turbulence. It is normally assumed that the wavefront distortion in the phase reference pulses is identical to the wavefront distortion in the quantum signals, which are multiplexed during transmission. However, in real‐world deployments, there can exist a relative wavefront error (WFE) between the reference pulses and quantum signals, which, among other deleterious effects, can severely limit secure key transfer in satellite‐to‐Earth CV‐QKD. In this work, we introduce machine learning‐based wavefront correction algorithms, which utilize multi‐plane light conversion for decomposition of the reference pulses and quantum signals into the Hermite‐Gaussian (HG) basis, then estimate the difference in HG mode phase measurements. Through detailed simulations of the Earth‐satellite channel, we demonstrate that our algorithm can identify and compensate for any relative WFEs that may exist. We quantify the gains available in our algorithm in terms of the CV‐QKD secure key rate. We show channels where positive secure key rates are obtained using our algorithms, while information loss without wavefront correction would result in null key rates.
Coherent measurement of quantum signals used for continuous-variable (CV) quantum key distribution (QKD) across satellite-to-ground channels requires compensation of phase wavefront distortions caused by atmospheric turbulence. One compensation technique involves multiplexing classical reference pulses (RPs) and the quantum signal, with direct phase measurements on the RPs then used to modulate a real local oscillator (RLO) on the ground - a solution that also removes some known attacks on CV-QKD. However, this is a cumbersome task in practice - requiring substantial complexity in equipment requirements and deployment. As an alternative to this traditional practice, here we introduce a new method for estimating phase corrections for an RLO by using only intensity measurements from RPs as input to a convolutional neural network, mitigating completely the necessity to measure phase wavefronts directly. We show that the phase correction accuracy needed to provide for non-zero secure key rates through satellite-to-ground channels is achieved by our intensity-only measurements. Our work shows, for the first time, how artificial intelligence algorithms can replace phase-measuring equipment in the context of CV-QKD delivered from space, thereby delivering an alternate deployment paradigm for this global quantum-communication application.
This article offers a solution to the fragmentation problem through a unified model and simulation showing how Adaptive Optics (AO) improves both classical and quantum communications. Free-space optical links can carry Quantum Key Distribution (QKD) over distances that cannot be reached with fiber; however, atmospheric turbulence corrupts the wavefront. For a single-mode quantum receiver, this drives the quantum bit error rate above the security threshold before detector noise can even be considered. AO addresses this by restoring the wavefront and recovering the coupling loss. The theory, mitigation techniques, and quantum security analysis needed to understand this are spread across three research communities that rarely cite one another: atmospheric turbulence and AO theory, classical modulation over fading channels, and BB84 quantum key distribution. We consolidate and develops all three topics in order to trace the chain from wavefront error to bit error rate and secret key rate. We survey six families of turbulence mitigation and provide an assessment of their suitability for single-mode quantum links. In addition, we survey the free-space QKD experimental record, from terrestrial hops to satellite downlinks. A wave optics case study of a representative 500-km Low Earth Orbit (LEO) downlink, corrected by a closed-loop Shack–Hartmann and deformable-mirror receiver at 1.55 μm ties the review together. Across a turbulence sweep, the correction stabilizes single-mode coupling near its physical ceiling, while the uncorrected channel varies by more than an order of magnitude. When carried into the downlink budget, this lifts the quantum link across the 11% security bound at 12 of 15 turbulence conditions where the uncorrected link yields no key, thereby restoring a secure quantum bit error rate in a narrow 4.2–4.9% band throughout and a secret key rate of 7.6–11.2 kbit/s while simultaneously widening the margin of the co-propagating classical channel above its forward error correction threshold.
An available trick to mitigate the interference of environmental noise in quantum communications is to modulate signals with time-polarization multiplexing. Conversely, due to effects of the atmospheric turbulence in free space, the polarization of signals fluctuates randomly, resulting in feasible information leakage when direct polarization demultiplexing is carried out at the receiver, drowning out the noise-contained signals. For enhancing the practical security of the continuous-variable quantum key distribution (CVQKD), we propose a machine learning (ML) approach for optimization of the dynamic polarization control (DPC) of signals transmitted through atmospheric turbulence. An optimal DPC scheme can be adaptively adjusted with ML algorithms, which is based on the received signals at the receiver for solving the loophole problem of information leakage since it provides an accurate response to the polarization changes regarding the anamorphic signals. The performance of the CVQKD system can be increased in terms of secret key rates and maximal transmission distance as well. Numerical simulation shows the positive effect of the ML-based DPC while taking into account the secret key rate of the CVQKD system. The ML-based DPC effectively reduces the feasibility of information leakage and hence results in an increased secret key rate of the practical CVQKD system.