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arXiv:2502.09920 · International Conference on Quantum Communications, Networking, and Computing (QCNC)

Machine Learning for Phase Estimation in Satellite-to-Earth Quantum Communication

Nathan K. Long, Robert Malaney, Kenneth J. Grant

Published Mar 31, 2025• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.1109/qcnc64685.2025.00080

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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.

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Continuous-variable quantum key distribution (CV-QKD) holds promise for enhancing security in communication networks. However, obtaining a higher secure key rate poses challenges, particularly in reliable phase estimation. So, it is very necessary for CV-QKD implementations with independent local oscillator (LO) to employ carrier recovery along with precise phase estimation. Our methodology combines extended Kalman filters (EKF) with recurrent neural networks (RNNs) to enhance the accuracy of phase recovery for locally generated LO signals. Using numerical simulations, we evaluate the achievable secret key rates for different transmission distances and line widths. The proposed method achieves a phase error of approximately 1 × 10–4, leading to positive secure key rates for distances up to 40 km. This method of phase tracking solves the problem and is effective in real-time deployment of CV-QKD in communication networks.

Optica Applicata•Jun 10, 2025•0 citations
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.
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 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.
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.
Abstract For a practical continuous-variable quantum key distribution (CV-QKD) system, the optimization of modulation variance is crucial for promoting protocol performance. The optimization relies on algorithms like local search in general. But the efficiency of local search methods is limited in low latency and limited computing power scenarios due to their high computational consumption. Hence, this optimization approach is infeasible for satellite-based CV-QKD due to satellites’ low power feature. In this paper, a neural network model that directly predicting the optimal modulation variance in nearly real time is proposed for free space gaussian modulated CV-QKD protocols. This work enhances the feasibility of implementing CV-QKD in low-Earth-orbit satellite scenarios, where typical link durations of few seconds demand rapid parameter optimization. Moreover, a simulation platform for free space CV-QKD protocol, which employs the precise orbital model to extract the elevation angle and the transmission length, is designed and developed to generate training sets that make the neural network model more practical. Our work can be used as a foundation to support parameter prediction for future quantum communication satellite missions.
Continuous variable quantum key distribution (CV-QKD) offers information-theoretic secure key sharing between two parties. The sharing of a phase reference frame is an essential requirement for coherent detection in CV-QKD. Due to the potential attacks related to transmitting the local oscillator (LO) alongside quantum signals, there has been a focus on using local LOs (LLOs) to establish a shared phase reference. In this work, we develop a new noise model of a current state-of-the-art LLO scheme in the context of the satellite-to-Earth channel. In doing this, we encapsulate detailed phase-screen calculations that determine the coherent efficiency - a critical parameter in free-space CV-QKD that characterizes the wavefront aberrations caused by atmospheric turbulence. Using our new noise model we then determine the CV-QKD key rates for the satellite-to-Earth channel, secure under general attacks in the finite-size regime of the LLO scheme. Our results are of practical importance for next-generation quantum-enabled satellites that utilize multi-photon technology as opposed to single-photon technology.
Continuous-variable quantum key distribution (CV-QKD) holds promise for enhancing security in communication networks. However, obtaining a higher secure key rate poses challenges, particularly in reliable phase estimation. So, it is very necessary for CV-QKD implementations with independent local oscillator (LO) to employ carrier recovery along with precise phase estimation. Our methodology combines extended Kalman filters (EKF) with recurrent neural networks (RNNs) to enhance the accuracy of phase recovery for locally generated LO signals. Using numerical simulations, we evaluate the achievable secret key rates for different transmission distances and line widths. The proposed method achieves a phase error of approximately 1 × 10–4, leading to positive secure key rates for distances up to 40 km. This method of phase tracking solves the problem and is effective in real-time deployment of CV-QKD in communication networks.