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Fading-Memory Quaternion-Based Kalman Filter for Quantum Channel PMD Compensation

Omar Alnaseri, Yassine Himeur, Salem Titouni, Jens Timmermann, Shadi Atalla

Published Jan 1, 2026• 0 citations

Abstract

Polarization mode dispersion in optical fibers corrupts polarization-encoded quantum states through random, time- and frequency-varying rotations. Because quantum states cannot be directly measured and reused without disturbance, practical mitigation requires adaptive compensation that operates on a physically consistent state representation. This paper models the quantum polarization channel and compensator directly in the quaternion domain, where unit quaternions naturally represent SU(2) polarization rotations and preserve the unit-norm constraint of valid quantum states. Building on this model, we introduce a fading-memory quaternion multiplicative extended Kalman filter, which is a quaternion formulation augmented with a fading (forgetting) mechanism that selectively discounts outdated information so the estimator can rapidly re-track varying rotation and recover quickly after abrupt polarization changes. A comparative study against quaternion least mean squares, quaternion recursive least squares, and a baseline quaternion multiplicative extended Kalman filter shows that Kalman-based approaches achieve faster convergence and higher broadband spectral fidelity, while the proposed fading-memory multiplicative extended Kalman filter provides the strongest robustness in dynamic conditions by improving re-lock behavior and reducing outage events under stronger drift. These results indicate that quaternion-based channel modeling combined with fading-memory Kalman estimation is a strong approach for quantum-state-preserving polarization mode dispersion compensation in realistic fiber links.

DOI: 10.1109/access.2026.3675938

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The polarization mode dispersion (PMD) in optical fibers poses a major challenge for maintaining the fidelity of quantum states for quantum communications. In this work, a comprehensive model linking the probability of quantum measurement errors (infidelity) to PMD is developed and validated by experimental measurements of differential group delay and quantum bit error rate (QBER). Our research proposes effective methods to mitigate PMD effects for broadband entangled photons and evaluates the impact of higher-order PMD effects. The model provides an experimentally verified framework for the optimization of commercial quantum key distribution systems in deployed fiber-optic lines.

We present a method for characterizing depolarization in fiber channels carrying broadband polarization-encoded optical signals. Wavelength-dependent polarization mode dispersion maps each input polarization to a trajectory on the Poincaré sphere; we show that the singular value decomposition of the band-averaged rotation matrix yields, in closed form, the optimal input states, the associated mutually unbiased measurement bases, and the resulting projection error probabilities. The three singular values provide a compact, bandwidth-dependent channel signature that distinguishes first- from higher-order dispersion, and yield the bandwidth at which the worst-case error probability reaches 3% as a practical filtering budget. We perform a second-order analysis of the band average that treats the two higher-order mechanisms: variation of the differential group delay at a fixed principal-state axis and wander of that axis with wavelength. We characterize 12 deployed fiber links in Masdar City and demonstrate mitigation by concatenating two channels through a single polarization controller, a step towards nonlocal compensation. The analysis is implemented in an openly available Python library for fiber-channel characterization.