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arXiv:2610.27363

Quaternion-Valued Adaptive Projection Statistics for Neural Receivers in Dual-Polarization Free-Space Quantum Communications

Anders Buvarp, Stefan Werner

Published Oct 19, 2026• 0 citations
arXivHTMLPDF

Abstract

Dual-polarization free-space quantum communication receivers produce two coupled complex heterodyne streams. We develop robust quaternion receiver methods for such links under fading, polarization mixing, calibration mismatch, impulsive contamination, and other non-Gaussian disturbances. The four polarization and quadrature components are encoded as quaternion-valued samples. We formulate an identifiable effective channel model, Quaternion-Valued Projection Statistics (QVPS), and Adaptive QVPS (AQVPS), which augments samplewise projection outlyingness with robust local second-order descriptors. Robust complex and quaternion channel estimators use radial Huber weighting, while QVPS and AQVPS are evaluated separately as disturbance diagnostics. Neural experiments compare matched real-, complex-, quaternion-, and widely linear complex-valued receivers. Robust estimation reduces sensitivity to non-Gaussian contamination. Local second-order descriptors improve detection of the tested localized disturbances relative to QVPS, and a descriptor-only ablation slightly outperforms full AQVPS. Complex LMMSE gives the lowest evaluation MSE in the clean Gaussian SNR sweep, whereas the Quaternion NN, among the compared receivers with their nominal activations, gives the lowest mean evaluation MSE in the tested contaminated sweeps. Activation-matched experiments indicate that much of the nominal Quaternion NN robustness is attributable to bounded activation rather than quaternion parameterization alone. The methods are evaluated at the receiver processing level and do not constitute a composable CV-QKD security proof.

DOI
10.48550/arxiv.2610.27363

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Dual-polarization free-space quantum communication receivers produce two coupled complex heterodyne streams. We develop robust quaternion receiver methods for such links under fading, polarization mixing, calibration mismatch, impulsive contamination, and other non-Gaussian disturbances. The four polarization and quadrature components are encoded as quaternion-valued samples. We formulate an identifiable effective channel model, Quaternion-Valued Projection Statistics (QVPS), and Adaptive QVPS (AQVPS), which augments samplewise projection outlyingness with robust local second-order descriptors. Robust complex and quaternion channel estimators use radial Huber weighting, while QVPS and AQVPS are evaluated separately as disturbance diagnostics. Neural experiments compare matched real-, complex-, quaternion-, and widely linear complex-valued receivers. Robust estimation reduces sensitivity to non-Gaussian contamination. Local second-order descriptors improve detection of the tested localized disturbances relative to QVPS, and a descriptor-only ablation slightly outperforms full AQVPS. Complex LMMSE gives the lowest evaluation MSE in the clean Gaussian SNR sweep, whereas the Quaternion NN, among the compared receivers with their nominal activations, gives the lowest mean evaluation MSE in the tested contaminated sweeps. Activation-matched experiments indicate that much of the nominal Quaternion NN robustness is attributable to bounded activation rather than quaternion parameterization alone. The methods are evaluated at the receiver processing level and do not constitute a composable CV-QKD security proof.
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