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arXiv:2610.27358

Variational Blind Equalization for Dual-Polarization Free-Space Quantum Communications

Anders Buvarp, Stefan Werner

Published Oct 19, 2026• 0 citations
arXivHTMLPDF

Abstract

Dual-polarization free-space quantum communication links require receiver equalization under polarization mixing, fading, phase variation, and limited channel supervision. This paper investigates variational blind and semi-blind equalization using VISTA (Variational Inference for Signal Tracking and Adaptation), a variational autoencoder-based probabilistic physical parameter estimator. In the semi-blind branch, channel-relevant statistics are mapped to the underlying 2x2 complex polarization channel. We compare forward KL, reverse KL, Average Jeffreys, Max-KL, and Adaptive Jeffreys regularization and analyze directional KL asymmetry and the local effect of the regularization weight zeta. Over 500 paired Monte Carlo trials, forward KL is nearly insensitive to zeta, whereas reverse and symmetric objectives exhibit low-error regions followed by degradation under stronger regularization. At zeta = 3 x 10^-5, Average Jeffreys reduces median channel NRMSE by approximately 4.8% relative to forward KL at the same weight. Reduced KL asymmetry does not necessarily imply lower channel error. A separate fully blind QPSK receiver estimates a direct equalizer from received data only. Over 3000 paired trials, the VISTA variants have nearly identical median aligned block-NMSE, while their lower mean aligned block-NMSE relative to the CMA-plus-separation baseline is concentrated in difficult, large-error trials. Direct-W optimization with Adam reproduces most of this mean reduction. In the fully blind benchmark, the tested weak regularizers provide no resolved improvement over unregularized VISTA.

DOI
10.48550/arxiv.2610.27358

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Dual-polarization free-space quantum communication links require receiver equalization under polarization mixing, fading, phase variation, and limited channel supervision. This paper investigates variational blind and semi-blind equalization using VISTA (Variational Inference for Signal Tracking and Adaptation), a variational autoencoder-based probabilistic physical parameter estimator. In the semi-blind branch, channel-relevant statistics are mapped to the underlying 2x2 complex polarization channel. We compare forward KL, reverse KL, Average Jeffreys, Max-KL, and Adaptive Jeffreys regularization and analyze directional KL asymmetry and the local effect of the regularization weight zeta. Over 500 paired Monte Carlo trials, forward KL is nearly insensitive to zeta, whereas reverse and symmetric objectives exhibit low-error regions followed by degradation under stronger regularization. At zeta = 3 x 10^-5, Average Jeffreys reduces median channel NRMSE by approximately 4.8% relative to forward KL at the same weight. Reduced KL asymmetry does not necessarily imply lower channel error. A separate fully blind QPSK receiver estimates a direct equalizer from received data only. Over 3000 paired trials, the VISTA variants have nearly identical median aligned block-NMSE, while their lower mean aligned block-NMSE relative to the CMA-plus-separation baseline is concentrated in difficult, large-error trials. Direct-W optimization with Adam reproduces most of this mean reduction. In the fully blind benchmark, the tested weak regularizers provide no resolved improvement over unregularized VISTA.
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.
Satellite networks and quantum communications offer complementary opportunities for enhanced operations. Quantum communications provide security for the transmissions between satellites and ground stations; while the free-space link of satellite networks provide the potential of long distance transmission of quantum bits (qubit) for space communications. However, with the promising advantages of the two approaches, challenges remain to fully develop quantum-based satellite communications such as robust and reliable information detection which is difficult to achieve due to the movement of satellites. In this paper, a tracking algorithm is proposed for polarization-encoded quantum satellite communications where polarization states are used to determine the bit transfer between the transmitter and receiver. The polarization tracking is essential for the decoding of a qubit and the quantum key distribution (QKD). A practical channel model for free-space quantum communications is adopted in this paper. With the estimated polarization, a novel dynamic polarization compensation scheme is also proposed. The results show that our methods can accurately estimate the polarization, providing much lower quantum bit error rate (QBER) by compensation, as compared with the direct qubit detection without polarization tracking and compensation scheme.
This paper investigates a quantum extension of classical Multiple-Input Multiple-Output (MIMO) communication in which the conventional linear channel model is replaced by a parameterized multi-qubit unitary transformation. Within this framework, interference is represented through coherent quantum interactions rather than additive signal coupling. To recover transmitted information, a Variational Quantum Circuit (VQC) receiver is introduced that learns an approximate inverse channel transformation through supervised variational optimization. The proposed system is evaluated under realistic noisy intermediate-scale quantum (NISQ) conditions incorporating depolarizing noise, thermal relaxation, and measurement imperfections, and its performance is compared with that of standard classical detection methods. The results reveal a trade-off between the two approaches: classical detectors achieve substantially lower bit-error rates across much of the investigated parameter range but exhibit pronounced performance degradation for specific channel configurations, whereas the VQC receiver maintains a more uniform error profile as channel complexity increases, albeit at a higher average BER. These findings suggest that variational quantum receivers are not a direct replacement for classical detection methods, but rather a complementary approach that may offer increased performance stability in communication scenarios characterized by strong coupling and complex interference patterns.
Accurate channel estimation is a fundamental requirement for high-performance wireless communication systems, where conventional deep learning approaches often suffer from excessive trainable parameters and high memory cost as antenna and subcarrier dimensions scale up. This paper proposes a quantum machine learning (QML)-based channel estimation framework that addresses this scalability challenge through a compact hybrid quantum-classical architecture. An 8-qubit quantum neural network (QNN) based on a parameterized quantum circuit (PQC) encodes received pilot-domain features using both Cartesian and polar components through Hadamard initialization and rotation-based quantum encoding, and learns channel representations using trainable variational rotations and controlled-Z (CZ) entanglement. The Pauli-Z measurement outputs are then processed by a lightweight classical dense head to produce the final channel estimate. The proposed QNN is compared with a classical deep neural network (DNN) and a QNN without hidden dense layers over a 2 × 1 Rayleigh fading multiple-input single-output (MISO) channel across an SNR range of 10 dB to 30 dB. Simulation results show that the proposed hybrid QNN achieves the lowest normalized mean square error (NMSE) across the entire evaluated SNR range while using only 1,012 trainable parameters, compared with 3,356 for the DNN. At 30 dB SNR, the proposed QNN achieves the lowest NMSE of approximately − 20.24 dB, compared with approximately − 17.54 dB for the DNN baseline. An ablation study further confirms that the dense post-processing head is essential for accurate regression from raw quantum measurement outputs. These results suggest that compact hybrid quantum-classical estimators offer a promising direction for accurate and parameter-efficient channel estimation in next-generation wireless communication systems.
Quantum metrology holds the potential to enhance magnetic field sensing beyond current limits. However, in the presence of realistic noise, this advantage degrades to the Standard Quantum Limit. While recent algorithmic and variational techniques attempt to recover this scaling, they are hindered by stringent control requirements on the probe state that are infeasible in the near term, or by barren plateaus and interpretability issues inherent to black-box variational quantum circuits. Here, we introduce Variational Inference and Sensing with Twin Ansätze (VISTA), a closed-loop protocol that combines passive sensing, or where the probe state is left to evolve without any active control, with physics-informed variational optimization. In the VISTA framework, a probe state evolves under a Lindbladian master-equation, and is compared, via the Swap test, to a parameterized ``quantum twin", a shallow quantum circuit designed to mimic the underlying pure-state or Lindbladian master-equation dynamics. By restricting the optimization space to the physical parameters of interest, VISTA circumvents barren plateaus. We demonstrate that by coupling the protocol with a classical optimizer and high shot counts, VISTA can temporarily achieve near-Heisenberg scaling for moderately noisy qubits over a finite range of system sizes. Furthermore, we introduce a Quasi-Normalization technique that sharpens the loss gradients, enabling simultaneous extraction of both the coherent signal θθθ and the environmental noise rate γγγ with low absolute error. Finally, we extend VISTA to the multi-parameter vector metrology regime, enabling simultaneous parameter extraction from a transverse-magnetic-field Hamiltonian. By eliminating the need for complex, open-loop control and processing, VISTA offers a highly practical, resource-efficient framework for near- to intermediate-term quantum sensors.
A major challenge in near-term quantum computing is its application to large real-world datasets due to scarce quantum hardware resources. One approach to enabling tractable quantum models for such datasets involves finding low-dimensional representations that preserve essential information for downstream analysis. In classical machine learning, variational autoencoders (VAEs) facilitate efficient data compression, representation learning for subsequent tasks, and novel data generation. However, no quantum model has been proposed that exactly captures all of these features for direct application to quantum data on quantum computers. Some existing quantum models for data compression lack regularization of latent representations, thus preventing direct use for generation and control of generalization. Others are hybrid models with only some internal quantum components, impeding direct training on quantum data. To address this, we present a fully quantum framework, $\ensuremath{\zeta}$-QVAE, which encompasses all the capabilities of classical VAEs and can be directly applied to map both classical and quantum data to a lower-dimensional space, while effectively reconstructing much of the original state from it. Our model utilizes regularized mixed states to attain optimal latent representations. It accommodates various divergences for reconstruction and regularization. Furthermore, by accommodating mixed states at every stage, it can utilize the full data density matrix and allow for a training objective defined on probabilistic mixtures of input data. Doing so, in turn, makes efficient optimization possible and has potential implications for private and federated learning. In addition to exploring the theoretical properties of $\ensuremath{\zeta}$-QVAE, we demonstrate its performance on representative genomics and synthetic data. Our results indicate that $\ensuremath{\zeta}$-QVAE consistently learns representations that better utilize the capacity of the latent space and exhibits similar or better performance compared with matched classical models.