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.
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.
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.
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.
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.
Continuous-variable quantum key distribution (CV-QKD) shows potential for the rapid development of an information-theoretic secure global communication network; however, the complexities of CV-QKD implementation remain a restrictive factor. Machine learning (ML) has recently shown promise in alleviating these complexities. ML has been applied to almost every stage of CV-QKD protocols, including ML-assisted phase error estimation, excess noise estimation, state discrimination, parameter estimation and optimization, key sifting, information reconciliation, and key rate estimation. This survey provides a comprehensive analysis of the current literature on ML-assisted CV-QKD. In addition, the survey compares the ML algorithms assisting CV-QKD with the traditional algorithms they aim to augment, as well as providing recommendations for future directions for ML-assisted CV-QKD research.
A global continuous-variable quantum key distribution (CV-QKD) network can be established using a series of satellite-to-Earth channels. Increased performance in such a network is provided by performing coherent measurement of the optical quantum signals using a real local oscillator, calibrated locally by encoding known information on transmitted reference pulses and using signal phase error estimation algorithms. The speed and accuracy of the signal phase error estimation algorithm are vital to practical CV-QKD implementation. Our work provides a framework to analyze long short-term memory neural network (NN) architecture parameterization, with respect to the quantum Cramér-Rao uncertainty bound of the signal phase error estimation, with a focus on reducing the model complexity. More specifically, we demonstrate that signal phase error estimation can be achieved using a low-complexity NN architecture, without significantly sacrificing accuracy. Our results significantly improve the real-time performance of practical CV-QKD systems deployed over satellite-to-Earth channels, thereby contributing to the ongoing development of the Quantum Internet.